Trigonometry Examples

Solve for x cos(x)^2+sin(x)^2=(x/r)^2+(y/r)^2
Step 1
Move all the expressions to the left side of the equation.
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from both sides of the equation.
Step 2
Simplify .
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Step 2.1
Rearrange terms.
Step 2.2
Apply pythagorean identity.
Step 2.3
Simplify each term.
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Step 2.3.1
Apply the product rule to .
Step 2.3.2
Apply the product rule to .
Step 3
Solve for .
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Step 3.1
Move all terms not containing to the right side of the equation.
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Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Add to both sides of the equation.
Step 3.2
Divide each term in by and simplify.
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Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left side.
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Step 3.2.2.1
Dividing two negative values results in a positive value.
Step 3.2.2.2
Divide by .
Step 3.2.3
Simplify the right side.
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Step 3.2.3.1
Simplify each term.
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Step 3.2.3.1.1
Divide by .
Step 3.2.3.1.2
Move the negative one from the denominator of .
Step 3.2.3.1.3
Rewrite as .
Step 3.3
Multiply both sides by .
Step 3.4
Simplify.
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Step 3.4.1
Simplify the left side.
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Step 3.4.1.1
Cancel the common factor of .
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Step 3.4.1.1.1
Cancel the common factor.
Step 3.4.1.1.2
Rewrite the expression.
Step 3.4.2
Simplify the right side.
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Step 3.4.2.1
Simplify .
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Step 3.4.2.1.1
Apply the distributive property.
Step 3.4.2.1.2
Multiply by .
Step 3.4.2.1.3
Cancel the common factor of .
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Step 3.4.2.1.3.1
Move the leading negative in into the numerator.
Step 3.4.2.1.3.2
Cancel the common factor.
Step 3.4.2.1.3.3
Rewrite the expression.
Step 3.5
Solve for .
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Step 3.5.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.5.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3.5.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 3.5.3.1
First, use the positive value of the to find the first solution.
Step 3.5.3.2
Next, use the negative value of the to find the second solution.
Step 3.5.3.3
The complete solution is the result of both the positive and negative portions of the solution.