Trigonometry Examples

Solve for θ in Degrees 16cos(theta)^2-25=0
Step 1
Add to both sides of the equation.
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4
Simplify .
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Step 4.1
Rewrite as .
Step 4.2
Simplify the numerator.
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Step 4.2.1
Rewrite as .
Step 4.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 4.3
Simplify the denominator.
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Step 4.3.1
Rewrite as .
Step 4.3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 5
The complete solution is the result of both the positive and negative portions of the solution.
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Step 5.1
First, use the positive value of the to find the first solution.
Step 5.2
Next, use the negative value of the to find the second solution.
Step 5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 6
Set up each of the solutions to solve for .
Step 7
Solve for in .
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Step 7.1
The range of cosine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 8
Solve for in .
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Step 8.1
The range of cosine is . Since does not fall in this range, there is no solution.
No solution
No solution