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# Trigonometry Examples

To find the between the x-axis and the line between the points and , draw the triangle between the three points , , and .

Opposite :

Adjacent :

A mixed number is an addition of its whole and fractional parts.

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 .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Simplify the expression.

Apply the product rule to .

Raise to the power of .

Raise to the power of .

Apply the product rule to .

Raise to the power of .

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

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 .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Rewrite as .

Simplify the numerator.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Simplify the denominator.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

therefore .

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Combine and .

Multiply by .

Combine and .

Move the negative in front of the fraction.

Approximate the result.