February 02, 2017
Precalc Warm Up #
6-5
Rewrite using the sum formulas:
1. sin 2u = sin (u + u)
2. cos 2u
3. tan 2u
February 02, 2017
Rewrite using the sum and difference formulas:
a. sin 2u
b. cos 2u
c. tan 2u
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Double angle formulas
sin(2x) = 2 sin x cos x
cos (2x)
= 1 - 2 sin2 x
= 2 cos2 x - 1
= cos2 x - sin2 x
February 02, 2017
Some problems are well suited to using the
double angle formulas. Solve:
2 cos x + sin 2x = 0
2 cosx + 2 sin x cos x = 0
2 cos x (1 + sin x) = 0
2 cos x = 0
or
1 + sin x = 0
cos x = 0
sin x = -1
π/2, 3π/2
February 02, 2017
2
Solve: cos 2x = 2 sin x on
2
2
1 - 2 sin x = 2 sin x
1
2
= 4 sin x
2
1/4 = sin x
± 1/2 = sin x
x = π/6, 5π/6, 7π/6, 11π/6
February 02, 2017
Use the double angle formulas in reverse order.
4 sinx cosx = 1
Because of the 1, the factors here don't help us. But
if you rewrite it using the double angle formula you
get:
2(2sinx cosx) = 1
2 sin 2x
=1
sin 2x
= 1/2
February 02, 2017
Classwork and Homework