Trigonometry Examples

Find the Exact Value tan(22.5)
Rewrite as an angle where the values of the six trigonometric functions are known divided by .
Apply the tangent half-angle identity.
Change the to because tangent is positive in the first quadrant.
The exact value of is .
The exact value of is .
Simplify .
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Multiply by .
Multiply and .
Expand the denominator using the FOIL method.
Simplify.
Apply the distributive property.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Combine and .
Simplify each term.
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Apply the distributive property.
Multiply .
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Simplify each term.
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Rewrite as .
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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
Multiply by .
Cancel the common factor of and .
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Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Apply the distributive property.
Multiply by .
Add and .
Subtract from .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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