# Trigonometry Examples

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Step 1

Use the definition of tangent to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

Step 2

Find the hypotenuse of the unit circle triangle. Since the opposite and adjacent sides are known, use the Pythagorean theorem to find the remaining side.

Step 3

Replace the known values in the equation.

Step 4

Step 4.1

One to any power is one.

Hypotenuse

Step 4.2

Raise to the power of .

Hypotenuse

Step 4.3

Add and .

Hypotenuse

Hypotenuse

Step 5

Use the definition of sine to find the value of .

Step 6

Substitute in the known values.

Step 7

Step 7.1

Multiply by .

Step 7.2

Combine and simplify the denominator.

Step 7.2.1

Multiply by .

Step 7.2.2

Raise to the power of .

Step 7.2.3

Raise to the power of .

Step 7.2.4

Use the power rule to combine exponents.

Step 7.2.5

Add and .

Step 7.2.6

Rewrite as .

Step 7.2.6.1

Use to rewrite as .

Step 7.2.6.2

Apply the power rule and multiply exponents, .

Step 7.2.6.3

Combine and .

Step 7.2.6.4

Cancel the common factor of .

Step 7.2.6.4.1

Cancel the common factor.

Step 7.2.6.4.2

Rewrite the expression.

Step 7.2.6.5

Evaluate the exponent.

Step 8

The result can be shown in multiple forms.

Exact Form:

Decimal Form: