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cos(6x)= sin(90-6x)= sin(3x-9)
sin values are equal u can equate the angles
90-6x=3x-9
99=9x
x=11

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6x + 3x - 9 = 90

x = 11
sin(66) = sin(24) in degrees

sin(x) = cos(y) are co-functions, meaning angles x and y are complementary.

@RobZBHayes : exactly!

You mean it is the same type of problem, right?

But not the same exact problem.

For sin(pi/2 - 6x) = sin(3x - 9) the angles are equal so
pi/2 - 6x = 3x - 9

Solve for x

What are your answer choices?

Yes, that's what I got

pi/2 - 6x = 3x - 9
180/2 - 6x = 3x - 9
90 + 9 = 6x + 3x
99 = 9x
99/9 = x
11 = x

Remember, pi = 180

Those are properties of co-functions

So the covertion of sin to cos and vice versa is always pi/2-x and pi always equals 180?

pi = 180 because the length of pi is a semicircle having a measure of 180 degrees.

Trig is a shortened way of saying Trigonometry

Which means every angle is an angle in a triangle?

The equation in that form is the definition of a co-function. That's how you know.

http://www.barstow.edu/lrc/tutorserv/handouts/045%20Trigonometric%20Properties.pdf

It's as simple as that.

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