Question

Giveb cos x = -1/5 and x is the third quadrant, matcy the trigonometric ratios with their respective values

Answer 1

I think the answer is 15 and Put an number 0 150

Answer 2

1. The trigonometric ratios for
`\( \cos(x) = -1/5 \)`in the third quadrant are:

`\( \sin(x) = -√(24)/5 \)`

`\( \tan(x) = √(24) \)`

`\( \tan(x) = √(24) \)`
`\( \tan(x) = √(24) \)`

`\( \sec(x) = -5 \)`

`\( \cot(x) = 1/√(24) \).`

Step-by-step explanation:

Given that
`\( \cos(x) = -1/5 \)` and x is in the third quadrant, we can determine the other trigonometric ratios using the relationships between trigonometric functions. In the third quadrant,
`\( \sin(x) \)` is negative, and
`\( \tan(x) \), \( \csc(x) \), \( \sec(x) \), and \( \cot(x) \)`are positive.

Using the Pythagorean identity
`\( \sin^2(x) + \cos^2(x) = 1 \), we find \( \sin(x) = -√(24)/5 \)`. The tangent
`\( \tan(x) \)` is calculated as
`\( \tan(x) = \sin(x)/\cos(x) = -√(24) \).`

The reciprocal functions are then obtained as
`\( \csc(x) = 1/\sin(x) = -5/√(24) \), \( \sec(x) = 1/\cos(x) = -5 \), and \( \cot(x) = 1/\tan(x) = 1/√(24) \).` Thus, the complete set of trigonometric ratios for
`\( \cos(x) = -1/5 \)` in the third quadrant is
`\( \sin(x) = -√(24)/5 \), \( \tan(x) = √(24) \), \( \csc(x) = -5/√(24) \), \( \sec(x) = -5 \), and \( \cot(x) = 1/√(24) \).`