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

What is the rule for the cosine function?

A. y=2 cos 4theta

B. y=4 cos 2theta

C. y=-4 cos 3theta

D. y=1/4 cos 2theta

Answer 1

I think the answer would be:
B) y= 4 cos 2 theta

Answer 2

The rule for the cosine function is:

B)
`y=4 \cos 2\theta`

Explanation:

We are given the property of angle theta as follows:

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

Also, we will check by keeping these conditions in each of the given options.

A)

`y=2\cos 4\theta`

when θ=0 we have:

`y=2\cos 0\\\\y=2\\eq 4`

Hence, option: A is incorrect.

C)

`y=-4\cos 3\theta`

when θ=0 we have:

`y=-4\cos 0\\\\y=-4\\eq 4`

Hence, option: C is incorrect.

D)

`y=(1)/(4) \cos 2\theta`

when θ=0 we have:

`y=(1)/(4)\cos 0\\\\y=(1)/(4)\\eq 4`

Hence, option: D is incorrect.

B)

`y=4\cos 2\theta`

when θ=0 we have:

`y=4\cos 0\\\\y=4`

and similarly the other conditions also gets satisfied.

Hence, option: B is the correct answer.