Question

Solve for x in the given interval.

CSC X= -1,, for 3pi < x < 4pi


A. 5pi/2

B.3pi

C.7pi/2

D.4pi

Answer 1

7pi/2

Explanation:

Given the expression cosec x = -1

I'm trigonometry csecx = 1/sinx

The equation becomes

1/sin(x) = -1

Sinx = -1

x = arcsin(-1)

x = -90°

x is negative in the third and 4th interval

Third interval;

x = 180+90

x = 270°

x = 3pi/2

Since the angle should be within 3pi < x < 4pi

Add 2pi to the angle

x = 2pi+ 3pi/2

x = 7pi/2

Hence the required angle is 7pi/2