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
16°
18°
22°
36°
The relationship between the sine and cosine of complementary angles is given by:
sin(90° - x) = cos(x)
In order to use this relationship to determine the value of x in the given expression, we need to rewrite the expression in terms of complementary angles.
sin(3x+10°) = cos(2x−10°)
First, we rewrite cos(2x−10°) as sin(90° - (2x - 10°)) using the relationship.
sin(3x+10°) = sin(90° - (2x - 10°))
Now, we can set the angles inside the sine functions equal to each other.
3x + 10° = 90° - (2x - 10°)
Simplifying the equation, we get:
3x + 10° = 90° - 2x + 10°
5x = 80°
Dividing both sides by 5, we find:
x = 16°
Therefore, the value of x is 16°.