Final answer:
To solve the equation sin(x)° = cos(x+6)°, we use the complementary angle identity and find that x = 42.
Step-by-step explanation:
To find the value of x in the equation sin(x)° = cos(x+6)°, we need to utilize trigonometric identities and properties. In particular, we can use the complementary angle identity which states that sin(90° - θ) = cos(θ). Thus, for the equation sin(x)° = cos(x+6)° to hold true, x and (x+6)° must be complementary angles. So we must solve the equation 90 - x = x + 6. After rearranging terms, we get 2x = 84, which simplifies to x = 42.