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3.Trigonometrical Ratios, Functions and Identities
medium
If $\tan \theta = \frac{{ - 4}}{3},$ then $\sin \theta = $
A
$-4/5$ but not $4/5$
B
$-4/5 $ or $4/5$
C
$4/5$ but not $-4/5$
D
None of these
(IIT-1979)
Solution
(b) Since ${\rm{cose}}{{\rm{c}}^2}\theta = 1 + {\cot ^2}\theta = 1 + \frac{9}{{16}} = \frac{{25}}{{16}}$
$\left( \because {\tan \theta = – \frac{4}{3}} \right)$
${\sin ^2}\theta = \frac{1}{{{\rm{cose}}{{\rm{c}}^2}\theta }} = \frac{{16}}{{25}} $
$\Rightarrow \sin \theta = \pm \frac{4}{5},$
Both the values are acceptable, since $\tan \theta = – \frac{4}{3}\,\,$
$\,i.e.,\theta $ lies in ${2^{nd}}$ or ${4^{th}}$ quadrant.
Standard 11
Mathematics
