Trigonometry Examples

Solve for x (2cos(x)-3sin(x)^2)=13
Step 1
Subtract from both sides of the equation.
Step 2
Replace the with based on the identity.
Step 3
Simplify each term.
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Step 3.1
Apply the distributive property.
Step 3.2
Multiply by .
Step 3.3
Multiply by .
Step 4
Subtract from .
Step 5
Reorder the polynomial.
Step 6
Substitute for .
Step 7
Factor by grouping.
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Step 7.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 7.1.1
Factor out of .
Step 7.1.2
Rewrite as plus
Step 7.1.3
Apply the distributive property.
Step 7.2
Factor out the greatest common factor from each group.
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Step 7.2.1
Group the first two terms and the last two terms.
Step 7.2.2
Factor out the greatest common factor (GCF) from each group.
Step 7.3
Factor the polynomial by factoring out the greatest common factor, .
Step 8
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 9
Set equal to and solve for .
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Step 9.1
Set equal to .
Step 9.2
Add to both sides of the equation.
Step 10
Set equal to and solve for .
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Step 10.1
Set equal to .
Step 10.2
Solve for .
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Step 10.2.1
Subtract from both sides of the equation.
Step 10.2.2
Divide each term in by and simplify.
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Step 10.2.2.1
Divide each term in by .
Step 10.2.2.2
Simplify the left side.
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Step 10.2.2.2.1
Cancel the common factor of .
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Step 10.2.2.2.1.1
Cancel the common factor.
Step 10.2.2.2.1.2
Divide by .
Step 10.2.2.3
Simplify the right side.
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Step 10.2.2.3.1
Move the negative in front of the fraction.
Step 11
The final solution is all the values that make true.
Step 12
Substitute for .
Step 13
Set up each of the solutions to solve for .
Step 14
Solve for in .
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Step 14.1
The range of cosine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 15
Solve for in .
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Step 15.1
The range of cosine is . Since does not fall in this range, there is no solution.
No solution
No solution