Trigonometry Examples

Solve for y 3/2arccos(y/8)=pi
Step 1
Multiply each term in by to eliminate the fractions.
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Step 1.1
Multiply each term in by .
Step 1.2
Simplify the left side.
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Step 1.2.1
Combine and .
Step 1.2.2
Cancel the common factor of .
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Step 1.2.2.1
Factor out of .
Step 1.2.2.2
Cancel the common factor.
Step 1.2.2.3
Rewrite the expression.
Step 1.2.3
Cancel the common factor of .
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Step 1.2.3.1
Cancel the common factor.
Step 1.2.3.2
Rewrite the expression.
Step 1.3
Simplify the right side.
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Step 1.3.1
Combine and .
Step 1.3.2
Move to the left of .
Step 2
Take the inverse arccosine of both sides of the equation to extract from inside the arccosine.
Step 3
Simplify the right side.
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Step 3.1
Simplify .
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Step 3.1.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
Step 3.1.2
The exact value of is .
Step 4
Multiply both sides of the equation by .
Step 5
Simplify both sides of the equation.
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Step 5.1
Simplify the left side.
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Step 5.1.1
Cancel the common factor of .
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Step 5.1.1.1
Cancel the common factor.
Step 5.1.1.2
Rewrite the expression.
Step 5.2
Simplify the right side.
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Step 5.2.1
Simplify .
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Step 5.2.1.1
Cancel the common factor of .
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Step 5.2.1.1.1
Move the leading negative in into the numerator.
Step 5.2.1.1.2
Factor out of .
Step 5.2.1.1.3
Cancel the common factor.
Step 5.2.1.1.4
Rewrite the expression.
Step 5.2.1.2
Multiply by .