What is the number of cycles of y=9cos(θ/4+3π/2)+4 between 0 and 2π?

Choice C) 1/4

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Work Shown:

Let's rearrange terms a bit to say the following:

The last equation is in the form

where,

We only need to worry about the value of B.

In this case, B = 1/4

So,

The period is 8pi. Every 8pi units, a full cycle is completed.

However, we're not going from 0 to 8pi, but instead from 0 to 2pi.

The given interval is 2pi units wide. This is (2pi)/(8pi) = 1/4 of a full cycle. This is why choice C is the answer.

here you hope this .

step-by-step explanation:

hypotenuse = √(15² + 8²)

=  √(225 +64)

=  √(289) = 17

sin(x) = cos(y) = 8/17

they are identical so long as you are doing the sine of one angle and the cosine of the only other angle that isn't the right angle.