Question

For a particular angle theta, the cosine function f(x) = a cos b(theta) has the following values within one cycle of the function.

f(0) = 4; f(pi/4) = 0; f(pi/2) = -4; f(3pi/4) = 0; f(pi) = 4


What is the rule for the cosine function?


A) y= 2 cos 4 theta

B) y= 4 cos 2 theta

C) y= -4 cos 3 theta

D) y= 1/4cos 2 theta

Answer 1

For function
`f(x)=a\cos b\theta` we have that
`f(0) =4,\ f( (\pi)/(2) )=-4,\ f(\pi)=4`. This means that period of cosine function is π. Then from the formula for period
`T= (2\pi)/(b)` you obtain that
`\pi= (2\pi)/(b)` and b=2.

So, the function is
`f(x)=a\cos 2\theta`. If f(0)=4, then
`a\cos0=4` and, respectively, a=4.
Answer:
`f(x)=4\cos 2\theta`.