Question

If sec x = -2 and π < x < 3π/2, find the values of all the other five trigonometric functions.

Answer 1

Given: sec x = -2

Given that: \(\pi<x<\frac{3\pi}{2}\)

So, x lies in IIIrd Quadrant. So, sin and cos will be negative but tan will be positive.

Now, we know that

cos x = \(\frac{1}{sec\,x}\)

Putting the values, we get

cos x = \(\frac{1}{-2}\)  .....(i)

We know that,

cos² x + sin² x = 1

Putting the values, we get

Since, x in IIIrd quadrant and sinx is negative in IIIrd quadrant

∴ sin x = \(-\frac{\sqrt{3}}{2}\)

Now,

tan x = \(\frac{sin\,x}{cos\,x}\)

Putting the values, we get

Hence, the values of other trigonometric Functions are: