{"id":63,"date":"2026-08-05T05:36:02","date_gmt":"2026-08-05T05:36:02","guid":{"rendered":"https:\/\/sqoolpapers.co.za\/notes\/trigonometry-gg12-maths\/"},"modified":"2026-08-22T16:06:10","modified_gmt":"2026-08-22T16:06:10","slug":"trigonometry-g12-maths-t4p2","status":"publish","type":"post","link":"https:\/\/repstaq.com\/study-guide-docs\/trigonometry-g12-maths-t4p2\/","title":{"rendered":"Trigonometry-G12-Maths-T4P2"},"content":{"rendered":"\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Trigonometry Study Notes<\/h2>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Compound Angles<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: Compound angles refer to the sum or difference of two angles, commonly represented as (A + B) or (A &#8211; B). The key formulas allow you to express trigonometric functions of compound angles in terms of the functions of their individual angles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Important Facts:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The main compound angle identities are:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Example: Calculate <span class=\"katex-eq\" data-katex-display=\"false\">\\sin(50^\\circ + 40^\\circ)<\/span>. Step 1: Write the formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\sin(A + B) = \\sin A \\cos B + \\cos A \\sin B\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Substitute the values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\sin(50^\\circ + 40^\\circ) = \\sin 50^\\circ \\cos 40^\\circ + \\cos 50^\\circ \\sin 40^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Simplify using a calculator.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= (0,7660 \\times 0,7660) + (0,6428 \\times 0,6428)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= 0,5868 + 0,4132 = 1\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Final answer:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\sin(90^\\circ) = 1\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Learners often use the wrong sign in the expanded formula. Remember: the sign within the formula for sine stays the same, for cosine it changes sign.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Always write out the full formula before substituting the values.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Double Angle Identities<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: Double angle identities are used for trigonometric expressions involving twice an angle, such as 2A.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Important Facts:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Main double angle formulas:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Example: Simplify <span class=\"katex-eq\" data-katex-display=\"false\">2\\sin 25^\\circ\\cos 25^\\circ<\/span>. Step 1: Use the double angle identity for sine.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\sin 2A = 2 \\sin A \\cos A\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n2\\sin 25^\\circ\\cos 25^\\circ = \\sin(2 \\times 25^\\circ)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= \\sin 50^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Forgetting to double the angle after applying the double angle formula, e.g., using <span class=\"katex-eq\" data-katex-display=\"false\">2\\sin\\theta\\cos\\theta = \\sin\\theta<\/span> instead of <span class=\"katex-eq\" data-katex-display=\"false\">\\sin2\\theta<\/span>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Know all three forms of the cosine double angle formula.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/sqooltutors.co.za\/sign-up-b\/\"><img decoding=\"async\" src=\"https:\/\/lmxddlwowqlsyucleuyv.supabase.co\/storage\/v1\/object\/public\/pdf_ads\/batch%201\/Doc%20Image%20Aug%2022,%202026,%2004_21_42%20PM%20(1).png\" alt=\"\"\/><\/a><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Reduction Formulae<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: Reduction formulae enable the simplification of trigonometric expressions involving (180\u00b0 \u00b1 x), (360\u00b0 \u00b1 x), (90\u00b0 \u00b1 x), etc.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Important Facts:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use the CAST diagram to determine the sign of the function in each quadrant.<\/li>\n\n\n\n<li>Key reduction identities include:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Example: Evaluate <span class=\"katex-eq\" data-katex-display=\"false\">\\cos(180^\\circ - 40^\\circ)<\/span>. Step 1: Write the formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\cos(180^\\circ - x) = -\\cos x\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Substitute values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\cos(180^\\circ - 40^\\circ) = -\\cos 40^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= -0,7660\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Using the wrong sign for the quadrant.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Always check the quadrant with a CAST diagram.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Trigonometric Identities<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: Trigonometric identities are equations true for all angles, used to simplify or prove trigonometric expressions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Important Identities:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span class=\"katex-eq\" data-katex-display=\"true\">\n\\sin^2\\theta + \\cos^2\\theta = 1\n<\/span><br><\/li>\n\n\n\n<li><span class=\"katex-eq\" data-katex-display=\"true\">\n1 + \\tan^2\\theta = \\sec^2\\theta\n<\/span><br><\/li>\n\n\n\n<li><span class=\"katex-eq\" data-katex-display=\"true\">\n1 + \\cot^2\\theta = \\csc^2\\theta\n<\/span><br><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Example: Prove that <span class=\"katex-eq\" data-katex-display=\"false\">1 - \\sin^2\\theta = \\cos^2\\theta<\/span>. Step 1: Start with the given expression.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n1 - \\sin^2\\theta\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Use the Pythagorean identity.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\sin^2\\theta + \\cos^2\\theta = 1\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Rearrange:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\cos^2\\theta = 1 - \\sin^2\\theta\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, <span class=\"katex-eq\" data-katex-display=\"false\">1 - \\sin^2\\theta = \\cos^2\\theta<\/span>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Not recognizing equivalent forms of identities.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Show all steps when proving identities in tests.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Solving Trigonometric Equations<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: Solving trig equations means finding all angles that satisfy a trigonometric equation, often within a given interval.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Steps:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Isolate the trig function first.<\/li>\n\n\n\n<li>Use reduction, factorisation or identities to simplify if needed.<\/li>\n\n\n\n<li>Find reference angle using calculator.<\/li>\n\n\n\n<li>Apply general solution based on function and interval.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Example: Solve <span class=\"katex-eq\" data-katex-display=\"false\">\\sin x = \\frac{1}{2}<\/span> for <span class=\"katex-eq\" data-katex-display=\"false\">0^\\circ \\leq x \\leq 360^\\circ<\/span>. Step 1: Find the reference angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\sin^{-1}(\\frac{1}{2}) = 30^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Write the general solution from the sine graph (since sine is positive in I and II quadrants).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nx = 30^\\circ \\quad\\text{or}\\quad x = 180^\\circ - 30^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nx = 30^\\circ \\text{ or } x = 150^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Forgetting all possible solutions in the range.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Use the CAST diagram to determine where the function is positive or negative.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">General Solutions<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: The general solution represents all possible solutions to a trig equation, using <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> as the integer constant.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">General Solution Forms:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For sine:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Example: Write the general solution for <span class=\"katex-eq\" data-katex-display=\"false\">\\tan x = 1<\/span>. Reference angle:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nx = 45^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">General solution:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nx = 45^\\circ + 180^\\circ k\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Mixing up the periodicity of sine\/cosine (360\u00b0) and tangent (180\u00b0).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Always include <span class=\"katex-eq\" data-katex-display=\"false\">k \\in \\mathbb{Z}<\/span> in your answer.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Two Dimensional Trigonometric Problems<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: Involves solving problems on a flat surface (plane) using angles and distances. Often uses right-angled triangles and trig ratios.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Applications:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Finding heights and distances (building, flagpole)<\/li>\n\n\n\n<li>Solving problems with bearings and directions.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Example: A ladder 5 m long rests against a wall making a 60\u00b0 angle with the ground. Find the height (h) where the ladder touches the wall. Step 1: Draw the triangle and identify the required parts. Step 2: Use sine ratio.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\sin 60^\\circ = \\frac{h}{5}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nh = 5 \\sin 60^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nh = 5 \\times 0,8660 = 4,33\\, \\text{m}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Not drawing or labelling a clear triangle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Always draw diagrams for worded trigonometry questions.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Three Dimensional Trigonometric Problems<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: Applies trigonometry to 3D objects like pyramids, poles, and buildings. Involves working with triangles in three dimensions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Applications:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Calculating lengths, angles, or heights in pyramids, prisms, and rectangular boxes.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Example: Given a pyramid with a square base, calculate the slant height using the vertical height and half of the base.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Use Pythagoras\u2019 theorem in the triangular face. Let the vertical height <span class=\"katex-eq\" data-katex-display=\"false\">h = 6<\/span> m, half the diagonal of base <span class=\"katex-eq\" data-katex-display=\"false\">a = 4<\/span> m.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\text{Slant height} = \\sqrt{6^2 + 4^2}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= \\sqrt{36 + 16}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= \\sqrt{52}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= 7,21\\, \\text{m}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Confusing the base length with the diagonal or not applying 2D trig first to find intermediate lengths.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Break the 3D problem into 2D triangles.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/sqooltutors.co.za\/sign-up-b\/\"><img decoding=\"async\" src=\"https:\/\/lmxddlwowqlsyucleuyv.supabase.co\/storage\/v1\/object\/public\/pdf_ads\/batch%201\/Doc%20Image%20Aug%2022,%202026,%2004_21_46%20PM%20(1).png\" alt=\"\"\/><\/a><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Sine Rule<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: The Sine Rule is used for non-right-angled triangles, relating the sides and their opposite angles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\frac{a}{\\sin A} = \\frac{b}{\\sin B} = \\frac{c}{\\sin C}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Example: In triangle PQR, <span class=\"katex-eq\" data-katex-display=\"false\">PQ = 10<\/span> cm, <span class=\"katex-eq\" data-katex-display=\"false\">\\angle R = 45^\\circ<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">QR = 8<\/span> cm, <span class=\"katex-eq\" data-katex-display=\"false\">\\angle P = 30^\\circ<\/span>. Find <span class=\"katex-eq\" data-katex-display=\"false\">\\angle Q<\/span>. Step 1: Write the Sine Rule.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\frac{PQ}{\\sin Q} = \\frac{QR}{\\sin P}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\frac{10}{\\sin Q} = \\frac{8}{\\sin 30^\\circ}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\frac{10}{\\sin Q} = \\frac{8}{0,5}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\frac{10}{\\sin Q} = 16\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\sin Q = \\frac{10}{16}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nQ = \\sin^{-1}(0,625) = 38,68^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Not matching sides and their opposite angles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Use the Sine Rule when you have side-angle-side (not enclosed) or angle-side-angle conditions.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Cosine Rule<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: The Cosine Rule is applicable to non-right-angled triangles when you know either three sides or two sides and the included angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\na^2 = b^2 + c^2 - 2bc \\cos A\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Example: Given triangle ABC with <span class=\"katex-eq\" data-katex-display=\"false\">AB = 8<\/span> cm, <span class=\"katex-eq\" data-katex-display=\"false\">AC = 5<\/span> cm, <span class=\"katex-eq\" data-katex-display=\"false\">\\angle BAC = 60^\\circ<\/span>. Find <span class=\"katex-eq\" data-katex-display=\"false\">BC<\/span>. Step 1: Write the Cosine Rule.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nBC^2 = AB^2 + AC^2 - 2(AB)(AC)\\cos BAC\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= 8^2 + 5^2 - 2 \\times 8 \\times 5 \\times \\cos 60^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= 64 + 25 - 80 \\times 0,5\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= 89 - 40 = 49\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nBC = 7\\, \\text{cm}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Using the wrong angle or not squaring the side.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Use the Cosine Rule for side-angle-side (enclosed angle) or side-side-side.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Area Rule<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Concept Explanation: The Area Rule allows you to find the area of any triangle using two sides and the included angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\text{Area} = \\frac{1}{2} ab \\sin C\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Example: Given triangle with <span class=\"katex-eq\" data-katex-display=\"false\">a = 6<\/span> cm, <span class=\"katex-eq\" data-katex-display=\"false\">b = 9<\/span> cm, <span class=\"katex-eq\" data-katex-display=\"false\">C = 30^\\circ<\/span>. Find the area.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Write the formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\text{Area} = \\frac{1}{2} ab \\sin C\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= \\frac{1}{2} \\times 6 \\times 9 \\times \\sin 30^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= 27 \\times 0,5\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n= 13,5\\, \\text{cm}^2\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common Mistake: Using the wrong angle, not the included angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Only use the Area Rule when dealing with two sides and the included angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">These notes are designed to help you quickly review major trigonometry concepts for Grade 12, with examples and explanations following the South African CAPS curriculum and standard exam conventions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trigonometry Study Notes Compound Angles Concept Explanation: Compound angles refer to the sum or difference of two angles, commonly represented as (A + B) or (A &#8211; B). The key formulas allow you to express trigonometric functions of compound angles in terms of the functions of their individual angles. Important Facts: Example: Calculate . Step [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_breakdance_hide_in_design_set":false,"_breakdance_tags":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-63","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"acf":{"document_name":"Trigonometry","grade":12,"subject":"Mathematics","term":4,"paper":2},"_links":{"self":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts\/63","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/comments?post=63"}],"version-history":[{"count":5,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts\/63\/revisions"}],"predecessor-version":[{"id":222,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts\/63\/revisions\/222"}],"wp:attachment":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/media?parent=63"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/categories?post=63"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/tags?post=63"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}