Question

If the angles
are represented in degrees, find both angles:
sin(x + 7) = cos(4x + 8)

Answer 1

sin(22 ∘ ) = cos(68∘ )

Explanation:

Sin(x+7)=cos(4x+8)

(x+7) + (4x+8) = 90

x + 7 + 4x + 8 = 90

5x + 15 = 90

−15 = −15

5x/5 = 75/5

x = 15

Answer: sin(22 ∘ ) = cos(68∘ )

Answer 2

x = -1/3

Explanation:

We have,

sin(x + 7) = cos(4x + 8)

We need to find the value of x.

We know that,

sin(90-x) = cosx

So,

sin(90-(x + 7)) = cos(4x + 8)

cos(x+7) = cos(4x + 8)

i.e.

(X+7) = (4x+8)

7-8 = 4x-x

-1 = 3x

x = -1/3