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3.Trigonometrical Ratios, Functions and Identities
medium
If $\cos x=-\frac{3}{5}, x$ lies in the third quadrant, find the values of other five trigonometric functions.
Option A
Option B
Option C
Option D
Solution
since $\cos x=-\frac{3}{5},$ we have sec $x=-\frac{5}{3}$
Now $\sin ^{2} x+\cos ^{2} x=1, \text { i.e., } \sin ^{2} x=1-\cos ^{2} x $
or $\sin ^{2} x=1-\frac{9}{25}=\frac{16}{25}$
Hence $\quad \sin x=\pm \frac{4}{5}$
since $x$ lies in third quadrant, $\sin x$ is negative. Therefore
$\sin x=-\frac{4}{5}$
which also gives
${\cos ec}\, x=-\frac{5}{4}$
Further, we have
$\tan x=\frac{\sin x}{\cos x}=\frac{4}{3} \text { and } \cot x=\frac{\cos x}{\sin x}=\frac{3}{4}$
Standard 11
Mathematics
