Precalculus Examples

Find the Other Trig Values in Quadrant III sin(x)=-1/2
Step 1
Use the definition of sine 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 adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.
Step 3
Replace the known values in the equation.
Step 4
Simplify inside the radical.
Tap for more steps...
Negate .
Adjacent
Raise to the power of .
Adjacent
Multiply by by adding the exponents.
Tap for more steps...
Multiply by .
Tap for more steps...
Raise to the power of .
Adjacent
Use the power rule to combine exponents.
Adjacent
Adjacent
Add and .
Adjacent
Adjacent
Raise to the power of .
Adjacent
Subtract from .
Adjacent
Adjacent
Step 5
Find the value of cosine.
Tap for more steps...
Use the definition of cosine to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
Step 6
Find the value of tangent.
Tap for more steps...
Use the definition of tangent to find the value of .
Substitute in the known values.
Simplify the value of .
Tap for more steps...
Dividing two negative values results in a positive value.
Multiply by .
Combine and simplify the denominator.
Tap for more steps...
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Tap for more steps...
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Step 7
Find the value of cotangent.
Tap for more steps...
Use the definition of cotangent to find the value of .
Substitute in the known values.
Simplify the value of .
Tap for more steps...
Dividing two negative values results in a positive value.
Divide by .
Step 8
Find the value of secant.
Tap for more steps...
Use the definition of secant to find the value of .
Substitute in the known values.
Simplify the value of .
Tap for more steps...
Move the negative in front of the fraction.
Multiply by .
Combine and simplify the denominator.
Tap for more steps...
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Tap for more steps...
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Step 9
Find the value of cosecant.
Tap for more steps...
Use the definition of cosecant to find the value of .
Substitute in the known values.
Divide by .
Step 10
This is the solution to each trig value.
Cookies & Privacy
This website uses cookies to ensure you get the best experience on our website.
More Information