Question

If cosx cos(pi/7) + sinx sin(pi/7) = -(sqrt(2))/2, then x can equal...? (Check all that apply) (Will give medal & fan!)

A. pi/4 + pi/7 + 2npi
B. 5pi/4 + pi/7 + 2npi
C. 7pi/4 + pi/7 + 2npi
D. 3pi/4 + pi/7 + 2npi

Answer 1

A straight up answer would be much appreciated, but an explanation is okay as well

Answer 2

@whpalmer4 when you get the chance can you help me?

Answer 3

I think the trig identity that will help here is this:

\[\cos(u-v) = \cos u \cos v + \sin u \sin v\]

Answer 4

How will that help me? I don't understand it. Like I see how the equation matches up with it but I just don't understand.

Answer 5

well, let's look at the first one. if \[x = \frac{\pi}{4} + \frac{\pi}7\]and we assume that the matching up means that \[\cos(x-\frac{\pi}{7}) = \cos x\cos\frac{\pi}7 +\sin x\sin\frac{\pi}7 = -\frac{\sqrt{2}}2\]

that means that \(\cos(x-\frac{\pi}7) = \cos(\frac{\pi}{4}+\frac{\pi}{7}-\frac{\pi}{7}) =\cos(\frac{\pi}{4})= -\frac{\sqrt{2}}{2}\)

Answer 6

but does \(\cos(\frac{\pi}{4}) = -\frac{\sqrt{2}}{2}\)?

Answer 7

I don't think so, no.

Answer 8

okay, so A is not a valid choice.

that pi/7 stuff looks scary until you realize that it disappears in the wash, so to speak...

Answer 9

So would it be 3pi/4 and 5pi/4?

Answer 10

Yes, that appears to be correct. Good job!

Answer 11

Yay! Thank you!