February 19, 2014
5.3
Sum and Difference Formulas
cos(u+v) = cosu cosv - sinu sinv
cos(u-v) = cosu cosv + sinu sinv
sin(u+v) = sinu cosv + cosu sinv
sin(u-v) = sinu cosv - cosu sinv
tan(u+v) = tanu + tanv
1 - tanu tanv
tan(u-v) = tanu - tanv
1 + tanu tanv
February 19, 2014
February 19, 2014
Write the expression as the sine, cosine, or tangent of an
angle.
1. cos94ocos18o+sin94osin18o
2. tan 3x - tan 2y
1 + tan 3x tan 2y
February 19, 2014
Examples. Simplify.
1. cos(
-x)
February 19, 2014
2. Confirm the cofunction identity.
sin(
2
-x)
= cos x
February 19, 2014
3. Find the exact value of sin 15.
February 19, 2014
4. Find the exact value of cos12
February 19, 2014
5. Find the exact value of sin (u + v) given:
sin u = 4
5
cos v = -12
13
0<u<
2
<v<
2
February 19, 2014
Evaluate:
cos (tan-11 + cos-1 x)
February 19, 2014
Prove the identity.
cos (x+h) - cos x
cos h - 1 - sin x sin h
= cos x
h
h
h