Trigonometry describes relationships between angles and sides. For a right-angled triangle, identify the side opposite the angle, the side adjacent to the angle and the hypotenuse.<\/p>\n\n\n\n
The mnemonic SOH CAH TOA helps learners remember these definitions.<\/p>\n\n\n\n
On the Cartesian plane, if the terminal arm of an angle passes through the point with coordinates shown below, the radius is calculated using the theorem of Pythagoras.<\/p>\n\n\n\n
The signs depend on the quadrant:<\/p>\n\n\n\n
The exact values of the special angles must be known.<\/p>\n\n\n\n
Example<\/strong><\/p>\n\n\n\nEvaluate the following without a calculator.<\/p>\n\n\n\n2<\/mn>sin<\/mi>30<\/mn>\u00b0<\/mo><\/msup>+<\/mo>cos<\/mi>60<\/mn>\u00b0<\/mo><\/msup><\/mrow><\/math><\/div>\n\n\n\nSubstitute the exact values.<\/p>\n\n\n\n=<\/mo>2<\/mn>(<\/mo>1<\/mn>2<\/mn><\/mfrac>)<\/mo>+<\/mo>1<\/mn>2<\/mn><\/mfrac><\/mrow><\/math><\/div>\n\n\n\n=<\/mo>3<\/mn>2<\/mn><\/mfrac><\/mrow><\/math><\/div>\n\n\n\nTrigonometric identities<\/h2>\n\n\n\nAn identity is true for every value for which both sides are defined. The two fundamental identities are:<\/p>\n\n\n\ntan<\/mi>\u03b8<\/mi>=<\/mo>sin<\/mi>\u03b8<\/mi><\/mrow>cos<\/mi>\u03b8<\/mi><\/mrow><\/mfrac><\/mrow><\/math><\/div>\n\n\n\nsin<\/mi>2<\/mn><\/msup>\u03b8<\/mi>+<\/mo>cos<\/mi>2<\/mn><\/msup>\u03b8<\/mi>=<\/mo>1<\/mn><\/mrow><\/math><\/div>\n\n\n\nUseful forms of the square identity include:<\/p>\n\n\n\nsin<\/mi>2<\/mn><\/msup>\u03b8<\/mi>=<\/mo>1<\/mn>\u2212<\/mo>cos<\/mi>2<\/mn><\/msup>\u03b8<\/mi><\/mrow><\/math><\/div>\n\n\n\ncos<\/mi>2<\/mn><\/msup>\u03b8<\/mi>
Evaluate the following without a calculator.<\/p>\n\n\n\n
Substitute the exact values.<\/p>\n\n\n\n
An identity is true for every value for which both sides are defined. The two fundamental identities are:<\/p>\n\n\n\n
Useful forms of the square identity include:<\/p>\n\n\n\n