Precalculus Examples

Find the Exact Value tan(255)
Step 1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 2
Split into two angles where the values of the six trigonometric functions are known.
Step 3
Apply the sum of angles identity.
Step 4
The exact value of is .
Step 5
The exact value of is .
Step 6
The exact value of is .
Step 7
The exact value of is .
Step 8
Simplify .
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Step 8.1
Multiply the numerator and denominator of the fraction by .
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Step 8.1.1
Multiply by .
Step 8.1.2
Combine.
Step 8.2
Apply the distributive property.
Step 8.3
Cancel the common factor of .
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Step 8.3.1
Cancel the common factor.
Step 8.3.2
Rewrite the expression.
Step 8.4
Multiply by .
Step 8.5
Simplify the denominator.
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Step 8.5.1
Multiply by .
Step 8.5.2
Multiply by .
Step 8.5.3
Cancel the common factor of .
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Step 8.5.3.1
Move the leading negative in into the numerator.
Step 8.5.3.2
Cancel the common factor.
Step 8.5.3.3
Rewrite the expression.
Step 8.6
Multiply by .
Step 8.7
Multiply by .
Step 8.8
Expand the denominator using the FOIL method.
Step 8.9
Simplify.
Step 8.10
Simplify the numerator.
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Step 8.10.1
Reorder terms.
Step 8.10.2
Raise to the power of .
Step 8.10.3
Raise to the power of .
Step 8.10.4
Use the power rule to combine exponents.
Step 8.10.5
Add and .
Step 8.11
Rewrite as .
Step 8.12
Expand using the FOIL Method.
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Step 8.12.1
Apply the distributive property.
Step 8.12.2
Apply the distributive property.
Step 8.12.3
Apply the distributive property.
Step 8.13
Simplify and combine like terms.
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Step 8.13.1
Simplify each term.
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Step 8.13.1.1
Multiply by .
Step 8.13.1.2
Move to the left of .
Step 8.13.1.3
Combine using the product rule for radicals.
Step 8.13.1.4
Multiply by .
Step 8.13.1.5
Rewrite as .
Step 8.13.1.6
Pull terms out from under the radical, assuming positive real numbers.
Step 8.13.2
Add and .
Step 8.13.3
Add and .
Step 8.14
Cancel the common factor of and .
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Step 8.14.1
Factor out of .
Step 8.14.2
Factor out of .
Step 8.14.3
Factor out of .
Step 8.14.4
Cancel the common factors.
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Step 8.14.4.1
Factor out of .
Step 8.14.4.2
Cancel the common factor.
Step 8.14.4.3
Rewrite the expression.
Step 8.14.4.4
Divide by .
Step 9
The result can be shown in multiple forms.
Exact Form:
Decimal Form: