Find exact solution for cot(5X)= -1 on the interval [0,2pi)

Find exact solutions for cot(5X)= -1 on the interval [0,2pi)?
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cot(5X)=-1, 1/tan(5X)=-1, tan(5X)=-1, 5X=3π/4 (quadrant 2), 7π/4 (quadrant 4). The quadrants are separated by π radians. 5X=(4n+3)π/4, where n is an integer.

There are 10 solutions (4n+3)π/20 in various quadrants (Q1-Q4):

n  X

0 3π/20 Q1

1 7π/20 Q1

2 11π/20 Q2

3 3π/4 Q2

4 19π/20 Q2

5 23π/20 Q3

6 27π/20 Q3

7 31π/20 Q4

8 7π/4 Q4

9 39π/20 Q4

by Top Rated User (1.1m points)

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