C H A P T E R 5 Analytic Trigonometry

490 Chapter 5 Analytic Trigonometry
Section 5.5 Multiple-Angle and Product-to-Sum Formulas
■ You should know the following double-angle formulas.
(a)
(b)
(b)
(b) 1 2 sin2 2 cos
u
2 cos 2u cos
u 1
2 u sin2 sin 2u 2 sin u cos u
u
2 tan u
(c) tan 2u
1 tan2 u
■ You should be able to reduce the power of a trigonometric function.
(a)
(b)
(c) tan
u u
u
■ You should be able to use the half-angle formulas. The signs of sin and cos depend on the quadrant in which lies.
2 2
2
2 cos
1 cos 2u
u
1 cos 2u
2 sin
1 cos 2u
u
2
2 1 cos 2u
u
2
(a)
(b)
(c)
sin u 1 cos u
± 2 2
cos u 1 cos u
± 2 2
tan u 1 cos u sin u
2 sin u 1 cos u
■ You should be able to use the product-sum formulas.
1
(a) sin u sin v cosu v cosu v
(b)
2
1
(c) sin u cos v sinu v sinu v
(d)
2
■ You should be able to use the sum-product formulas.
x y x y
(a) sin x sin y 2 sin (b)
2 cos
2
cos u cos v 1
cosu v cosu v
2
cos u sin v 1
sinu v sinu v
2
x y x y
sin x sin y 2 cos
2 sin
2
x y x y
x y
(c) cos x cos y 2 cos (d) cos x cos y 2 sin
2 cos
2
2
sin x y
2