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**Unformatted text preview: **our answers. y = cos(3x) and y = cos(5x) y = sin(2x) and y = √ √ 3 cos(x) and, 3 cos(x) 7. Unlike the previous problem, there seems to be no quick way to get the circular functions or
their arguments to match in the equation sin(x) cos x + cos(x) sin x = 1. If we stare at
2
2
it long enough, however, we realize that the left hand side is the expanded form of the sum
formula for sin x + x . Hence, our original equation is equivalent to sin 3 x = 1. Solving,
2
2
π
π
we ﬁnd x = π + 43 k for integers k . Two of these solutions lie in [0, 2π ): x = π and x = 53 .
3
3
Graphing y = sin(x) cos x + cos(x) sin x and y = 1 validates our solutions.
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2
8. With the absence of double angles or squares, there doesn’t seem to be much we can do.
However, since the arguments of the cosine and sine are the same, we can rewrite the left
√
hand side of this equation as a sinusoid.8 To ﬁt f (x) = cos(x) − 3 sin(x) to the form
A cos(ωt + φ) + B , we use what we learned in Example 10.5.3 and ﬁnd A = 2, B = 0, ω = 1
√
and φ = π . Hence, we can rewrite the equation cos(x) − 3 sin(x...

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