Trigonometry Examples

Factor out of .
Simplify the denominator.
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Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Turn the numerator into a polynomial.
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Rewrite.
Apply the distributive property.
Apply the distributive property.
Raise to the power of .
Use the power rule to combine exponents.
Add and to get .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and to get .
Turn the denominator into a polynomial.
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Rewrite.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and to get .
Multiply by to get .
Add and to get .
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Reorder and .
Add and to get .
Add and to get .
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
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Divide the highest order term in the dividend by the highest order term in divisor .
+
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Multiply the new quotient term by the divisor.
+
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++-
The expression needs to be subtracted from the dividend, so change all the signs in
+
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--+
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
+
+-+-+
--+
++
Pull the next term from the original dividend down into the current dividend.
+
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--+
+++
Divide the highest order term in the dividend by the highest order term in divisor .
++
+-+-+
--+
+++
Multiply the new quotient term by the divisor.
++
+-+-+
--+
+++
++-
The expression needs to be subtracted from the dividend, so change all the signs in
++
+-+-+
--+
+++
--+
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
++
+-+-+
--+
+++
--+
++
The final answer is the quotient plus the remainder over the divisor.
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