For any angle a we have the following relationships: Half angle formulas: Double angle formulas: We will use these formulas to determine the exact values of trig functions of certain angles in terms of half or double values. Proofs are available in all trig and pre-calculus texts. Two other formulas can be derived from and . By squaring both sides of the equations we can obtain and If we let A = we have .
Half angle formulas: Double angle formulas:
We can use a half angle formula noticing that . We have tan(15º) = tan() = .
We have tan(15º) = tan() = .
In the diagram of angle A shown below, the hypotenuse would be .
To find the sin(2A) we use the double angle formula
To find the we use the half angle formula . Since angle A is in quadrant four, we have . Dividing by 2 gives us which puts angle in quadrant two. Therefore the sine is positive and To find the we use the half angle formula .