,

The function is positive in the and quadrants. The function is positive in the and quadrants. The set of solutions for are limited to the since that is the only quadrant found in both sets.

Solution is in first quadrant.

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

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

Replace the known values in the equation.

Raise to the power of .

Opposite

One to any power is one.

Opposite

Multiply by .

Opposite

Subtract from .

Opposite

Rewrite as .

Factor out of .

Opposite

Rewrite as .

Opposite

Opposite

Pull terms out from under the radical.

Opposite

Opposite

Use the definition of sine to find the value of .

Substitute in the known values.

Use the definition of cosine to find the value of .

Substitute in the known values.

Use the definition of tangent to find the value of .

Substitute in the known values.

Divide by .

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 .

Move .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

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 .

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 .

Move .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

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 .

This is the solution to each trig value.

Find Trig Functions Using Identities sec(theta)=3 , tan(theta)>0