contestada

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

Respuesta :

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

Answer:

The rule for the cosine function is:

                  B)    [tex]y=4 \cos 2\theta[/tex]

Step-by-step explanation:

We are given the property of angle theta as follows:

   [tex]f(0)=4\ ;\ f(\dfrac{\pi}{4})=0\ ;\ f(\dfrac{\pi}{2})=-4\ ;\ f(\dfrac{3\pi}{4})=0\ ;\ f(\pi)=4[/tex]

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

A)

[tex]y=2\cos 4\theta[/tex]

when θ=0 we have:

[tex]y=2\cos 0\\\\y=2\neq 4[/tex]

Hence, option: A is incorrect.

C)

[tex]y=-4\cos 3\theta[/tex]

when θ=0 we have:

[tex]y=-4\cos 0\\\\y=-4\neq 4[/tex]

Hence, option: C is incorrect.

D)

[tex]y=\dfrac{1}{4} \cos 2\theta[/tex]

when θ=0 we have:

[tex]y=\dfrac{1}{4}\cos 0\\\\y=\dfrac{1}{4}\neq 4[/tex]

Hence, option: D is incorrect.

B)

[tex]y=4\cos 2\theta[/tex]

when θ=0 we have:

[tex]y=4\cos 0\\\\y=4[/tex]

and similarly the other conditions also gets satisfied.

       Hence, option: B is the correct answer.

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