Question

I NEED HELP ASAP!!! 100 POINTS

If 0 < f ≤ 90 and cos(22f − 1) = sin(7f + 4), what is the value of f?
f=3
f=4
f=5
f=6

Answer 1

A

Explanation:

We are given:

`\cos(22f-1)=\sin(7f+4)`

Recall the co-function identity:

`\sin(\theta)=\cos(90-\theta)`

Let θ = 7f + 4. So:

`\sin(7f+4)=\cos(90-(7f+4))`

Substitute:

`\cos(22f-1)=\cos(90-(7f+4))`

Remove the cosine:

`\displaystyle 22f-1=90-(7f+4)`

Distribute:

`22f-1=90-7f-4`

Subtract:

`22f-1=-7f+86`

Add 7f and 1 to both sides:

`29f=87`

Therefore:

`f=3`