Question

Cos (x + 16) = sin(3x – 2)

Answer 1

Cos (x+16) = sin(3x - 2)
Cos x + cos 16 = sin 3x - sin 2
Sin 2 + cos 16 = sin 3x - cos x
Sin 2 + cos 16 = x(sin 3 - cos 1)
0.0902 + (-0.9576) = x(0.1411-0.5403)

−0.8674 = −0.3992x
-0.3992 -0.3992

X = 2.17

Answer 2

x = 19

Explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55