Question

given the expression sin(3x+10degrees) = cos(2x-10degrees) which of the following uses the relationship between the sine and cosine of complementary angles to correctly determine the value of x

Answer 1

[AI-generated answer — Bot GPT 3.5]

The relationship between the sine and cosine of complementary angles states that sin(90° - θ) = cos(θ).

In the given expression sin(3x + 10°) = cos(2x - 10°), notice that there are angles that are complementary to each other. Let's identify these angles:

θ = 3x + 10°
90° - θ = 90° - (3x + 10°) = 80° - 3x

Since sin(θ) = cos(90° - θ), we can rewrite the expression as follows:

sin(θ) = cos(90° - θ)
sin(3x + 10°) = cos(80° - 3x)

Therefore, the correct relationship that uses the relationship between the sine and cosine of complementary angles to determine the value of x is sin(3x + 10°) = cos(80° - 3x).