Question

Determine the exact value for cos^-1(cos(7π/6)).
...& Also...
Determine the value of cos(-7π/4).

Answer 1

Well \[\Large \cos (\cos^{-1} (x))\]

Answer 2

=\[\Large x\]

Answer 3

\[\Large \cos(-x)=\cos(x)=\cos(-\frac{7\pi}{4})=\cos(\frac{7\pi}{4})\]

Answer 4

You can proceed from there right?

Answer 5

Since cos^-1() is the inverse function of cos(), you're just undoing it. It's like squaring the square root function, you get back what's inside.

To find the value of cos(-7π/4) you should realize that cosine is basically looking for the x-value of rotation on a circle and that a circle has 2π radians in all.

since they say -7π/4, that means you rotate around clockwise because of the negative sign for 7 quarters of pi.