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:

Answer 1

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

Answer 2

Answer:

The rule for the cosine function is:

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

Step-by-step explanation:

We are given the property of angle theta as follows:

   $f(0)=4\ ;\ f(\dfrac{\pi}{4})=0\ ;\ f(\dfrac{\pi}{2})=-4\ ;\ f(\dfrac{3\pi}{4})=0\ ;\ f(\pi)=4$

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:

$y=2\cos 0\\\\y=2\neq 4$

Hence, option: A is incorrect.

C)

$y=-4\cos 3\theta$

when θ=0 we have:

$y=-4\cos 0\\\\y=-4\neq 4$

Hence, option: C is incorrect.

D)

$y=\dfrac{1}{4} \cos 2\theta$

when θ=0 we have:

$y=\dfrac{1}{4}\cos 0\\\\y=\dfrac{1}{4}\neq 4$

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.