Math 1508 Name
D.Wilson
Section 5.4: Sum and Difference Formulas
sin(α+β) = sin αcos β+ sin βcos αsin(α−β) = sin αcos β−sin βcos α
cos(α+β) = cos αcos β−sin αsin βcos(α−β) = cos αcos β+ sin αsin β
1. (a) Find the exact value of sin31π
6
−
13π
3
(b) Find the exact value of sin31π
6−sin 13π
3
2. Write the expression as a sine, cosine, or tangent of an angle.
(a) sin (85◦) cos (165◦) + sin (165◦) cos (85◦)
(b) cos (85◦) cos (165◦) + sin (85◦) sin (165◦)
(c) sin 4π
9cos 7π
8+ sin 7π
8cos 4π
9
3. Find the exact value of the trigonometric function, given that sinu=−
15
17 and cos v=−
4
5, where u
is in QIV and vis in QIII.
cos(u+v)
