# Find the Other Trig Values in Quadrant IV sec(x) equals(two square root of three) divide three

Use the definition of secant to find the known sides of the unit circle right triangle. Each value's sign is defined by the quadrant.

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.

Clarify the expression.

Apply the product rule to .

Opposite

Raise to the power of .

Opposite

Opposite

Should be rewritten as .

Rewrite as .

Opposite

Apply the power rule when multiplying the exponents, .

Opposite

Add and .

Opposite

The common factor should be canceled of .

Cancel the common factor.

Opposite

First, divide by .

Opposite

Opposite

Solve the exponent.

Opposite

Opposite

Simplify the expression.

First, multiply by .

Opposite

Raise to the power of .

Opposite

Multiply by .

Opposite

Subtract from .

Opposite

Opposite

Opposite

Use the definition of sine to find the value of .

Substitute in the known values.

Simplify the value of .

The common factor should be canceled.

Cancel the common factor.

Reformulate the expression.

Put the negative in front of the fraction.

Use the definition of cosine to find the value of .

Substitute in the known values.

Simplify the value of .

Multiply by .

Combine and Clarify the denominator.

Multiply and .

Put .

Raise to the power of .

Raise to the power of .

Use the power rule to Add exponents.

Add and .

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

The common factor should be canceled.

Cancel the common factor.

Divide by .

Evaluate the exponent.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Use the definition of tangent to find the value of .

Substitute in the known values.

Move the negative in front of the fraction.

Use the definition of cotangent to find the value of .

Substitute in the known values.

Simplify the value of .

Multiply by .

Add and then 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.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Move the negative one from the denominator of .

Rewrite as .

Use the definition of cosecant to find the value of .

Substitute in the known values.

Simplify the value of .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Move the negative one from the denominator of .

Multiply by .

This is the solution to each trig value.

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