6.2 Cofunction and Double-Angle IdentitiesFri Dec 5

Do NowSimplify

(sinx + cosx)(sinx – cosx)

Cofunction Identities

•

Proof

• These can be proven using the sum and difference identities

• Proof of sin identity:

Cofunction Identities for Sine and Cosine

• Because of sine and cosine’s relationship, they have 2 more identities

Finding other identities

• Ex: Find an identity for

Ex2

• Find an identity for

Double Angle Identities

• Double-Angle identities give trig function values of 2x

• These are also proven using the sum identities

Ex

• Given tanx = -3/4, and x is in quadrant 2, find• 1) sin2x

• 2) cos2x

• 3) tan2x

• 4) The quadrant 2x lies in

Ex

• Find equivalent expressions for sin 3x in terms of x

Ex

• Find equivalent expressions of (cosx)^3 in terms of x or 2x, raised only to the first power

Closure

• Find an exact value of sin2x, cos2x, and tan2x if cosx = 5/13 in quadrant 1

• HW: p.553 #3-15, 23, 29 33

6.2 Half Angle IdentitiesMon Dec 8

• Do Now• Find the exact value of sin2x cos2x and tan2x

if tanx = -15/8 in quadrant 2

HW Review: p.553 #3-15, 23, 29 33

Half-Angle Identities

• We can find trig functions of angles that are half of what we already know how to find

Ex1

• Find the exact value of

Ex2

• Simplify

Ex3

• Simplify

Closure

• Given sinx = 4/5, evaluate sin (x/2)

• HW: p.554 #17-21 25 27 31