Trigonometry Examples

Find the Other Trig Values in Quadrant I sin(x)=8/10
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...
Step 4.1
Raise to the power of .
Adjacent
Step 4.2
Raise to the power of .
Adjacent
Step 4.3
Multiply by .
Adjacent
Step 4.4
Subtract from .
Adjacent
Step 4.5
Rewrite as .
Adjacent
Step 4.6
Pull terms out from under the radical, assuming positive real numbers.
Adjacent
Adjacent
Step 5
Cancel the common factor of and .
Tap for more steps...
Step 5.1
Factor out of .
Step 5.2
Cancel the common factors.
Tap for more steps...
Step 5.2.1
Factor out of .
Step 5.2.2
Cancel the common factor.
Step 5.2.3
Rewrite the expression.
Step 6
Find the value of cosine.
Tap for more steps...
Step 6.1
Use the definition of cosine to find the value of .
Step 6.2
Substitute in the known values.
Step 6.3
Cancel the common factor of and .
Tap for more steps...
Step 6.3.1
Factor out of .
Step 6.3.2
Cancel the common factors.
Tap for more steps...
Step 6.3.2.1
Factor out of .
Step 6.3.2.2
Cancel the common factor.
Step 6.3.2.3
Rewrite the expression.
Step 7
Find the value of tangent.
Tap for more steps...
Step 7.1
Use the definition of tangent to find the value of .
Step 7.2
Substitute in the known values.
Step 7.3
Cancel the common factor of and .
Tap for more steps...
Step 7.3.1
Factor out of .
Step 7.3.2
Cancel the common factors.
Tap for more steps...
Step 7.3.2.1
Factor out of .
Step 7.3.2.2
Cancel the common factor.
Step 7.3.2.3
Rewrite the expression.
Step 8
Find the value of cotangent.
Tap for more steps...
Step 8.1
Use the definition of cotangent to find the value of .
Step 8.2
Substitute in the known values.
Step 8.3
Cancel the common factor of and .
Tap for more steps...
Step 8.3.1
Factor out of .
Step 8.3.2
Cancel the common factors.
Tap for more steps...
Step 8.3.2.1
Factor out of .
Step 8.3.2.2
Cancel the common factor.
Step 8.3.2.3
Rewrite the expression.
Step 9
Find the value of secant.
Tap for more steps...
Step 9.1
Use the definition of secant to find the value of .
Step 9.2
Substitute in the known values.
Step 9.3
Cancel the common factor of and .
Tap for more steps...
Step 9.3.1
Factor out of .
Step 9.3.2
Cancel the common factors.
Tap for more steps...
Step 9.3.2.1
Factor out of .
Step 9.3.2.2
Cancel the common factor.
Step 9.3.2.3
Rewrite the expression.
Step 10
Find the value of cosecant.
Tap for more steps...
Step 10.1
Use the definition of cosecant to find the value of .
Step 10.2
Substitute in the known values.
Step 10.3
Cancel the common factor of and .
Tap for more steps...
Step 10.3.1
Factor out of .
Step 10.3.2
Cancel the common factors.
Tap for more steps...
Step 10.3.2.1
Factor out of .
Step 10.3.2.2
Cancel the common factor.
Step 10.3.2.3
Rewrite the expression.
Step 11
This is the solution to each trig value.