Find the degree measure of acute angle x if cos(40) = sin(x)?

You need to find an instance when sinx=cosx. Divide both sides by cosx sinx/cosx=1 sinx/cosx=tanx, so you need to determine when tanx=1 arctan1=45degrees both angles are 45 degrees or pi/4 radians (whichever you need) 45+45=90 or pi/4 + pi/4=pi/2.

It will be 90 degrees. Look at the graph of the sine function from 0 degrees to 90 degrees. Now look at the graph of the cosine function from 0 degrees to 90 degrees.

You'll notice that over that limited domain (from 0 to 90) they are mirror images of each other. If x is measured in degrees, then sin(x) = cos(90-x), and cos(x) = sin(90-x). Always.

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