# Trigonometry Examples

Find the Other Trig Values in Quadrant I
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.
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.
Replace the known values in the equation.
Rewrite as .
Rewrite as .
Hypotenuse
Apply the power rule and multiply exponents, .
Hypotenuse
Combine and .
Hypotenuse
Cancel the common factor of .
Cancel the common factor.
Hypotenuse
Divide by .
Hypotenuse
Hypotenuse
Evaluate the exponent.
Hypotenuse
Hypotenuse
One to any power is one.
Hypotenuse
Hypotenuse
Rewrite as .
Hypotenuse
Pull terms out from under the radical, assuming positive real numbers.
Hypotenuse
Hypotenuse
Find the value of sine.
Use the definition of sine to find the value of .
Substitute in the known values.
Find the value of cosine.
Use the definition of cosine to find the value of .
Substitute in the known values.
Find the value of cotangent.
Use the definition of cotangent to find the value of .
Substitute in the known values.
Simplify the value of .
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.
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.
Find the value of secant.
Use the definition of secant to find the value of .
Substitute in the known values.
Divide by .
Find the value of cosecant.
Use the definition of cosecant to find the value of .
Substitute in the known values.
Simplify the value of .
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.