# Find the Quadrant of the Angle (tan(175)-tan(55))/(1+tan(175)tan(55))

Find the Quadrant of the Angle (tan(175)-tan(55))/(1+tan(175)tan(55))
Convert the radian measure to degrees.
To convert radians to degrees, multiply by , since a full circle is or radians.
Simplify the numerator.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.
Evaluate to get .
Multiply by to get .
Evaluate to get .
Multiply by to get .
Subtract from to get .
Simplify the denominator.
Remove parentheses.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.
Evaluate to get .
Multiply by to get .
Evaluate to get .
Multiply by to get .
Subtract from to get .
Simplify the expression.
Divide by to get .
Multiply by to get .
Simplify .
Write as a fraction with denominator .
Multiply and to get .
Multiply by to get .
Move the negative in front of the fraction.
Factor out of .
Multiply by .
Separate fractions.
Replace with an approximation.
Divide by to get .
Divide by to get .
Multiply by to get .
Multiply by to get .
Convert to a decimal.
For angles smaller than , add to the angle until the angle is larger than .
The angle is in the third quadrant.