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## Another Problem 1

Find an angle in both radians and degrees whose cosine is equal to half the sine of the angle. Express your answer correctly rounded to 5 significant digits.

### Solution: 1.1071 radians, 63.435 degrees Sketch:

This is a problem that your calculator will not help unless you can translate the problem into an expression that can be evaluated. We picked this example so that you would see that your calculator will not solve the problems for you. You will need to use simple trigonometry and algebra to do this. In this problem, the key substitution is remembering that:

COS2 X + SIN2 X = 1

for any angle X.

You will need to know if your calculator is in radians mode or degrees mode to know what the answer is.

For example: with the calculator in radians mode, with pencil and paper, do the following:

1. Transform the problem statement into an equation, word for word; when you read this expression it should be as close to the problem statement as possible: x = COS-1 (.5* SIN x) (Note: x is on both sides of the equation.)

2. Take the COS of both sides, now the expression reads:
COS X = .5* SIN X

3. Square both sides, substitute 1 - SIN2 X for COS X, and simplify:
X = SIN-1 SQRT 4/5

4. NOW, use your calculator to evaluate the right side of this equation to find X:

You may either convert this number to degrees (hint: there are pi radians in 180 degrees), or you can put the calculator in degrees mode and resolve the last expression above to get 63.435 degrees, to 5 significant figures.

Next Try It Out Problem.

Developed by
Shodor
in cooperation with the Department of Chemistry,
The University of North Carolina at Chapel Hill