Question

Express \cos (27\pi )/(8) as a trigonometric function of an angle in Quadrant I.

Answer 1

For any value of $x$ and any integer $n$, $\cos(x+2n\pi)=\cos x$. Notice that

$\dfrac{27\pi}8=\dfrac{11\pi}8+2\pi$

which means

$\cos\dfrac{27\pi}8=\cos\dfrac{11\pi}8$

but $\dfrac{11\pi}8$ corresponds to an angle that falls in the third quadrant. Now,

$\dfrac{11\pi}8=\dfrac{3\pi}8+\pi$

and $\dfrac{3\pi}8$ does fall in the first quadrant. We use the fact that

$\cos(x+\pi)=-\cos x$

which tells us

$\cos\dfrac{27\pi}8=\cos\dfrac{11\pi}8=-\cos\dfrac{3\pi}8$

Answer 2

The correct answer is C on edge 2020!

Just got it right on the quiz, hope this helps!! :)