Question

WILL REWARD
Which cosine function has maximum of 4, a minimum of -4, and a period of 2pi/3?

A. y=4 cos 3 theta
B. y= 4 cos 2 theta/3
C. y=4 cos theta/3
D. y=4 cos 3 theta

Answer 1

Since \(\cos\) ranges between -1 and 1, it's really easy to see that any \(4\cos\) will have a min and max of -4 and 4 respectively.

A function \(\cos(B \times \theta)\) has period \(\frac{2\pi}{B}\).

So if we want the period to be \(\frac{2\pi}{3}\), \(B=3\).

Putting both conditions together, the function must be \(4\cos(\frac{\theta}{3})\), choice C.