Question

How do you solve `sin(x+37)° = cos(2x+8)°`?

Answer 1

`x = 15^@`
`x = - 61^@`

Explanation:

Applying the trig formula: sin a = cos (90 - a)
cos (2x + 8) = sin (x + 37) = cos (90 - x - 37) = cos (53 - x)
Property of the cosine function -->
`(2x + 8) = +- (53 - x)`
a. 2x + 8 = 53 - x
3x = 45
`x = 15^@`
b. 2x + 8 = - 53 + x
`x = - 61^@`
For general answers, add `k360^@`
Check by calculator.
x = 15 --> sin (x + 37) = sin 52 = 0.788
cos (2x + 8) = cos (38) = 0.788. Proved
x = - 61 --> sin (x + 37) = sin (- 24) = - sin 24 = - 0.407
cos (2x + 8) = cos (-122 + 8) = cos (- 114) = - 0.407. Proved