The value of csc x=-13/5.
Given that the sin x=-5/13 and x∈[3π/2 , 2π).
A trigonometric function is a real function that relates the angle of a right triangle to the ratio of the lengths of the two sides. The basic functions are sin, cos, tan, cot, sec, csc.
The given function is sin x=-5/13.
As we all know that sin x=1/csc x or csc x=1/sin x.
As it is given that x∈[3π/2 , 2π) that means x lies in fourth quadrant and in fourth quadrant sin and csc is negative in it.
So, we will apply this identity csc x=1/sin x, we get
csc x=1/(-5/13)
csc x=-13/5
And it also lies in x∈[3π/2 , 2π).
Hence, the value of csc x when sin x=-5/13 and x∈[3π/2 , 2π) is csc x=-13/5.
Learn more about the trigonometry function from here brainly.com/question/26221138
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