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?
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.