# Find the Trig Value cos(theta)=4/7

Use the definition of cosine 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.
Simplify .
Raise to the power of .
Opposite
Raise to the power of .
Opposite
Multiply by .
Opposite
Subtract from .
Opposite
Opposite
Find the value of sine.
Use the definition of sine to find the value of .
Substitute in the known values.
Find the value of tangent.
Use the definition of tangent 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.
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.
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.
This is the solution to each trig value.
Find the Trig Value cos(theta)=4/7