Download To learn the sum and difference trigonometric identities. Why

March 10, 2017
(5.3) Sum and Difference Identities
Objective: To learn the sum and difference trigonometric identities.
Why: These identities provide clear examples of how different
the algebra of functions can be different than the algebra of
real numbers.
March 10, 2017
Sum and Difference Identities
Obj: To learn the sum and difference trigonometric identities.
sin(u + v) = sinu cosv + cosu sinv
sin(u - v) = sinu cosv - cosu sinv
cos(u + v) = cosu cosv - sinu sinv
cos(u - v) = cosu cosv + sinu sinv
tan(u + v) =
tan(u - v) =
tanu + tanv
1 - tanu tanv
tanu - tanv
1 + tanu tanv
March 10, 2017
Obj: To learn the sum and difference trigonometric identities.
Identify the sum or difference identity used. Then write the expression as the
sine, cosine, or tangent of an angle.
o
o
o
1. cos94 cos18 +sin94 sin18
2. tan 3x - tan 2y
1 + tan 3x tan 2y
o
March 10, 2017
Obj: To learn the sum and difference trigonometric identities.
Examples. Simplify.
1. sin( π - x )
March 10, 2017
Obj: To learn the sum and difference trigonometric identities.
2. Use the sum and difference identities to prove the identity.
cos(
π
2
-x)
=
sin x
March 10, 2017
Obj: To learn the sum and difference trigonometric identities.
o
3. Find the exact value of sin 15 .
March 10, 2017
Obj: To learn the sum and difference trigonometric identities.
7π
4. Find the exact value of cos 12
March 10, 2017
Obj: To learn the sum and difference trigonometric identities.
5π
5. Find the exact value of tan 12
March 10, 2017
HW:
Obj: To learn the sum and difference trigonometric identities.
Pg.425: 3, 5, 7, 23, 25, 37, 47