If = - 4 3 , then = - Vidyadip

MCQ

If $\tan \theta = \frac{{ - 4}}{3},$ then $\sin \theta = $

A
$-4/5$ but not $4/5$
✓
$-4/5 $ or $4/5$
C
$4/5$ but not $-4/5$
D
None of these

✓

Answer

Correct option: B.

$-4/5 $ or $4/5$

b
(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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\mathop {\lim }\limits_{x \to 0} \left[ {\frac{1}{x} - \frac{{\log (1 + x)}}{{{x^2}}}} \right] =$

Let $A = \left( {\begin{array}{*{20}{c}}0&0&{ - 1}\\0&{ - 1}&0\\{ - 1}&0&0\end{array}} \right)$, the only correct statement about the matrix $A$ is

If $y = \frac{x}{{\ln \,|c\,x|}}$ (where $c$ is an arbitrary constant) is the general solution of the differential equation $\frac{{dy}}{{dx}} = \frac{y}{x}+ \phi \left( {\frac{x}{y}} \right)$ then the function $\phi \left( {\frac{x}{y}} \right)$ is :

The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is

For the three events $A, B$ and $C, P$ (exactly one of the events $A$ or $B$ occurs) = $P$ (exactly one of the events $B$ or $C$ occurs)= $P$ (exactly one of the events $C$ or $A$ occurs)= $p$ and $P$ (all the three events occur simultaneously) $ = {p^2},$ where $0 < p < 1/2$. Then the probability of at least one of the three events $A, B$ and $C$ occurring is

$7\log \left( {{{16} \over {15}}} \right) + 5\log \left( {{{25} \over {24}}} \right) + 3\log \left( {{{81} \over {80}}} \right)$ is equal to

Tangents $AB$ and $AC$ are drawn from the point $A(0,\,1)$ to the circle ${x^2} + {y^2} - 2x + 4y + 1 = 0$. Equation of the circle through $A, B$ and $C$ is

Solution of the equation $(x + \log y)dy + y\,dx = 0$ is

A bag contains, $7$ different Black balls .and $10$ different Red balls, if one by one ball are randomely drawn untill all black balls are not drawn, then probability that this process is completed in $12 ^{th}$ draw, is equal to

Let $y=m x+c, m>0$ be the focal chord of $y^{2}=-64 x$, which is tangent to $(x+10)^{2}+y^{2}=4$ Then, the value of $4 \sqrt{2}(\mathrm{~m}+\mathrm{c})$ is equal to $.....$