Trigonometry Examples

Solve for x sin(x/2) = square root of (1-cos(x))/2
Step 1
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2
To remove the radical on the left side of the equation, square both sides of the equation.
Step 3
Simplify each side of the equation.
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Step 3.1
Use to rewrite as .
Step 3.2
Simplify the left side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Multiply the exponents in .
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Step 3.2.1.1.1
Apply the power rule and multiply exponents, .
Step 3.2.1.1.2
Cancel the common factor of .
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Step 3.2.1.1.2.1
Cancel the common factor.
Step 3.2.1.1.2.2
Rewrite the expression.
Step 3.2.1.2
Simplify.
Step 4
Solve for .
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Simplify .
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Step 4.2.1
To write as a fraction with a common denominator, multiply by .
Step 4.2.2
Combine and .
Step 4.2.3
Combine the numerators over the common denominator.
Step 4.2.4
Simplify the numerator.
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Step 4.2.4.1
Multiply by .
Step 4.2.4.2
Move .
Step 4.2.4.3
Apply the cosine double-angle identity.
Step 4.2.4.4
Cancel the common factor of .
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Step 4.2.4.4.1
Cancel the common factor.
Step 4.2.4.4.2
Rewrite the expression.
Step 4.2.4.5
Subtract from .
Step 4.2.5
Divide by .
Step 4.3
Since , the equation will always be true for any value of .
All real numbers
All real numbers
Step 5
The result can be shown in multiple forms.
All real numbers
Interval Notation: