Find the Quadrant of the Angle (7pi)/5

Problem

(7*π)/5

Solution

1. Identify the standard quadrant boundaries in radians.

0<Quadrant I<π/2

π/2<Quadrant II<π

π<Quadrant III<(3*π)/2

(3*π)/2<Quadrant IV<2*π

2. Compare the given angle (7*π)/5 to the boundary π

π=(5*π)/5

(7*π)/5>(5*π)/5

(7*π)/5>π

3. Compare the given angle to the boundary (3*π)/2 by finding a common denominator.

(7*π)/5=(14*π)/10

(3*π)/2=(15*π)/10

(14*π)/10<(15*π)/10

(7*π)/5<(3*π)/2

4. Determine the quadrant based on the inequalities.

π<(7*π)/5<(3*π)/2

Final Answer

(7*π)/5∈Quadrant III

Want more problems? Check here!