84.
If f(x) = cox x and f(a) = 1/4, find the exact value of:
A. f(-a)
B. f(a) + f(a+ 2pi) + f(a-2pi)
88.
If f(x) csc x and f(a) = 2, find the exact value of
A. f(-a)
B. f(a) + f(a + 2pi) + f(a + 4pi)
$\displaystyle f(x) = \cos x$ is an even function meaning that: $\displaystyle f(x) = f(-x)$. You know what f(a) is so you can certainly find f(-a).
Also, cos x is a periodic function. If you've learned the unit circle, you can see that adding 2pi to your angle will have you end up at the exact same point on the unit circle. Same reasoning applies if you went backwards 2pi and went around the circle multiple times (i.e. multiples of 2pi). So: $\displaystyle f(x) = f(x \pm 2k\pi) \: \: k \in \mathbb{Z}$ (k is an integer)
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$\displaystyle f(x) = \csc x$ is an odd function, i.e. $\displaystyle f(-x) = -f(x)$. Use similar logic from above to arrive at your answers.
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