In a right triangle, Sin (4x + 10) º = Cos (6x) º. What is the value of x?

Step-by-step explanation:

These angles will be equal when each of them measures 45 degrees. On the unit circle, 45 degrees and reference angles of 45 degrees are the only places where sin and cos are the same. This means that

sin(4x + 10) = 45 and cos(6x) = 45

If we add the angles together (the angles being 4x+10 and 6x) we get a 90 degree angle. Thus,

4x + 10 + 6x = 90 and

10x = 80 so

x = 8. Let's try it out:

sin(4(8) + 10) = sin(42) = .6691306064 and

cos(6(8)) = cos(48) = .6691306064

Yay