Given the expression sin(3x+10°)=cos(2x−10°) , which of the following uses the relationship between the sine and cosine of complementary angles to correctly determine the value of x?(1 point) Responses 22° 22° 16° 16° 18° 18° 36° 36°
The relationship between the sine and cosine of complementary angles states that sin(x) = cos(90° - x).
In this case, we have sin(3x + 10°) = cos(2x - 10°).
From this, we can determine that 3x + 10° = 90° - (2x - 10°).
Simplifying this equation, we get 3x + 10° = 90° - 2x + 10°.
Combining like terms, we have 5x = 80°.
Dividing both sides by 5, we get x = 16°.
Therefore, the correct answer is 16°.