The graph of a trigonometric function satisfies the following conditions:

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

The graph of a trigonometric function

p(x)

satisfies the following conditions: (i) The maximum value

2

occurs at

x=\dfrac{\pi}{6}

. (ii) The minimum value

-2

occurs at

x=\dfrac{7\pi}{6}

. (iii) The function is zero at

x=\dfrac{2\pi}{3}

. Which of the following is a possible expression for

p(x)

? (a)

2\cos\left(x+\dfrac{\pi}{6}\right)

(b)

2\cos\left(x-\dfrac{\pi}{6}\right)

(c)

2\sin\left(x-\dfrac{\pi}{6}\right)

(d)

-2\cos\left(x-\dfrac{\pi}{6}\right)