Section+6.3

=Double-Angle and Half-Angle Identities= I. Derivation of Double-Angle Identities - To derive the double-angle identities, we let A = B in the sum identities II. Double-Angle Identities Sine Cosine Tangent sin(2A) = 2sinAcosA cos(2A) = cos^2(A) - sin^2(A) tan(2A) = 2tanA/ 1-tan^2(A) cos(2A) = 1-2sin^2A cos(2A) = 2cos^2(A) - 1 III. Finding Exact Values Using Double-Angle Identities - If sinx = -4/5 and cosx < 0, find (2x), cos(2x), and tan(2x)

The double-angle identities were used to derive the half-angle identities. We then used the half-angle identities to find certain values of trigonometric finctions, verify other trigonometric identities, and simplify trigonometric expressions.

We determine the sign, + or -, by first deciding which quadrant contains A/2 and then finding the sign of the indicated trigonometric function in that quadrant.

Recall that there are three form of the tangent half-angle identity. There is no need to memorize the other forms of the tangent half-angle identitiy, since they can be derived by first using the Pythagorean identity and algebraic manipulation.