If sin x = -24/25, then the value of tan x is _____

Question

\[ \text{If } \sin x=-\frac{24}{25}, \]

\[ \text{then the value of } \tan x \text{ is} \]

Using identity

\[ \sin^2x+\cos^2x=1 \]

\[ \left(-\frac{24}{25}\right)^2+\cos^2x=1 \]

\[ \frac{576}{625}+\cos^2x=1 \]

\[ \cos^2x=\frac{49}{625} \]

\[ \cos x=\pm\frac{7}{25} \]

Now,

\[ \tan x=\frac{\sin x}{\cos x} \]

\[ =\frac{-24/25}{\pm7/25} \]

\[ \tan x=\pm\frac{24}{7} \]

Since quadrant is not given, both signs are possible.

\[ \boxed{\pm\frac{24}{7}} \]

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