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

Answer 1

To use the relationship between the sine and cosine of complementary angles, we can rewrite the given equation using the identity: sin(theta) = cos(90 degrees - theta).

sin(3x + 10 degrees) = cos(2x - 10 degrees)

Using the identity, we can rewrite this as:

sin(3x + 10 degrees) = sin(90 degrees - (2x - 10 degrees))

Now, we can equate the angles:

3x + 10 degrees = 90 degrees - (2x - 10 degrees)

Simplifying the equation:

3x + 10 degrees = 90 degrees - 2x + 10 degrees

Combine like terms:

5x = 90 degrees

Divide by 5:

x = 18 degrees

So, the correct value of x is 18 degrees.