Trigonometry Examples

Solve for x -sin(x)=-cos(x)^2-1
Step 1
Move all the expressions to the left side of the equation.
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Step 1.1
Add to both sides of the equation.
Step 1.2
Add to both sides of the equation.
Step 2
Replace with .
Step 3
Solve for .
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Step 3.1
Simplify the left side.
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Step 3.1.1
Apply pythagorean identity.
Step 3.2
Replace the with based on the identity.
Step 3.3
Add and .
Step 3.4
Subtract from both sides of the equation.
Step 3.5
Divide each term in by and simplify.
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Step 3.5.1
Divide each term in by .
Step 3.5.2
Simplify the left side.
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Step 3.5.2.1
Dividing two negative values results in a positive value.
Step 3.5.2.2
Divide by .
Step 3.5.3
Simplify the right side.
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Step 3.5.3.1
Divide by .
Step 3.6
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.7
The complete solution is the result of both the positive and negative portions of the solution.
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Step 3.7.1
First, use the positive value of the to find the first solution.
Step 3.7.2
Next, use the negative value of the to find the second solution.
Step 3.7.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 3.8
Set up each of the solutions to solve for .
Step 3.9
Solve for in .
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Step 3.9.1
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 3.10
Solve for in .
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Step 3.10.1
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
No solution