If sin x=
Question:

If $\sin x=\frac{-24}{25}$, then the value of $\tan x$ is __________________ .

Solution:

Given $\sin x=\frac{-24}{25}$ i.e $\mathrm{x}$ lies in III or IV quadrant

$\sin x=\frac{A B}{A C}=\frac{-24}{25}$

Since $A C^{2}=A B^{2}+B C^{2}$

i. e $25^{2}=(24)^{2}+B C^{2}$

$\Rightarrow 625=576+B C^{2}$

$\Rightarrow B C^{2}=49$

$B C=\pm 7$

$\Rightarrow \tan x=\frac{24}{7}$ or $\tan x=\frac{-24}{7}$


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