Question

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

Answer 1

The correct answer is C on edge 2020!

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

Answer 2

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

`\frac{27\pi}8=\frac{11\pi}8+2\pi`

which means

`\cos\frac{27\pi}8=\cos\frac{11\pi}8`

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

`\frac{11\pi}8=\frac{3\pi}8+\pi`

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

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

which tells us

`\cos\frac{27\pi}8=\cos\frac{11\pi}8=-\cos\frac{3\pi}8`