# Find the Cosine (1/2,- square root of 3/2)

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

Opposite :

Adjacent :

Apply the product rule to .

One to any power is one.

Raise to the power of .

Rewrite as .

Multiply by .

Combine and simplify the denominator.

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Use to 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.

Simplify the numerator.

Combine using the product rule for radicals.

Multiply by .

Use the power rule to distribute the exponent.

Apply the product rule to .

Apply the product rule to .

Simplify the expression.

Raise to the power of .

Multiply by .

Rewrite as .

Use to 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.

Raise to the power of .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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 .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Rewrite as .

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.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Combine and simplify the denominator.

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Use to 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.

Approximate the result.

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