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°
To use the relationship between the sine and cosine of complementary angles, we need to find the value of the angle that satisfies sin(theta) = cos(90° - theta).
Let's compare the given expression sin(3x+10°) with the form sin(theta) = cos(90° - theta):
3x + 10° = 90° - (2x - 10°)
Simplifying the equation:
3x + 10° = 90° - 2x + 10°
Adding 2x to both sides:
5x + 10° = 90° + 10°
Subtracting 10° from both sides:
5x = 90°
Dividing both sides by 5:
x = 18°
Therefore, the correct value of x is 18°.