8/20/2019 I_Finding Solutions in an Interval for an Equation
With Sine and Cosine Using Double Angle
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Kwadwo Amankwa - 03/01/2016 6:37:58 AM PSTPreCalculus / Amankwa,
Kwadwo (Amankwa)
Finding solutions in an interval for an equation with sine and
cosine usingdouble-angle identities
Find all solutions of the equation in the interval .
Write your answer in radians in terms of .
If there is more than one solution, separate them with
commas.
The equation involves an input of and an input of .
We want to rewrite the equation so that it involves only inputs
of .
To do this, we can use one of the double-angle formulas for
cosine, .
Here is what we get.
We can factor the left-hand side and solve.
or
Cosine has the value at and .
It has the value at .
The answer is , , .
0, 2π
=+− cos θ cos 2θ 0
π
θ 2θ
θ
=cos 2θ −2cos2
θ 1
+− cosθ cos2θ = 0
+− cos θ −2cos2
θ 1 = 0
−2cos2
θ −cos θ 1 = 0
+2 cos θ 1 −cos θ 1 = 0
+2 cos θ 1 = 0 −cos θ 1 = 0
cosθ = −1
2cosθ = 1
−1
2
2π
3
4π
3
1 0
=θ 0 2π3
4π3
