Trigonometric Identities III Half Angles or t-formulae. By Mr Porter

Students should know these identities!. Pythagorean Identities of Trigonometry. For any angle θ Sum and Difference of Angles in Trigonometry. Double Angle Identities of Angles in Trigonometry. Students should know these identities!.

Students should learn these identities!. Half Angle Identities of Angles in Trigonometry. The half angle identities are usually referred to as the t-formulae. Given the definition, Using the double angle identities and setting, t 1 Using Pythagoras’ Theorem to find the hypotenuse. Then we can write the t-formulae. then Students should learn these identities!.

Example 1: If cos θ = , 0° ≤ θ ≤ 90°, find the exact value of tan . Using the t-formulae. Note: tan = t Rearrange and solve for ‘t’. 0°(360°) 90° 270° 180° θ° 180° — θ° 180° + θ° 360° — θ° S A C T Hence,

Example 2 If , express in terms of t : Substitute the t-formulae. Using the t-formulae. Note: Substitute the t-formulae. rearrange

Example 3 If , prove that Substitute the t-formulae. rearrange Using the t-formulae. Note: Substitute the t-formulae. rearrange

The t-formulae are used mainly to solve trigonometric equations.