Questions
$\dfrac{\cos(90-A)\sin(90-A)}{\tan (90-A)}$=
- $\sin^{2}A$
- $\cos^{2}A$
- $\sin A$
- $1$
The value of $ \displaystyle 36^{\circ} $ in radians is
- $ \displaystyle \frac{\pi }{2} $
- $ \displaystyle \frac{2\pi }{5} $
- $ \displaystyle \frac{\pi }{5} $
- $ 3\pi $
A unit radian is approximately equal to
- $57^{\circ} 17' 43"$
- $57^{\circ} 17' 45"$
- $57^{\circ} 17' 47"$
- $57^{\circ} 17' 49"$
The value of $\cot 15^{\circ} \cot 20^{\circ} \cot 70^{\circ} \cot 75^{\circ}$ is equal to
- $-1$
- $0$
- $1$
- $2$
Consider the following statements :
1. $1^o$ in radian measure is less than 0.02 radians.
2. 1 radian in degree measure is greater than $45^o$
Which of the above statements is/are correct ?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
If $\tan 45^{\circ} = \cot \theta$, then the value of $\theta$, in radians is
- $\pi$
- $\dfrac{\pi}{9}$
- $\dfrac{\pi}{4}$
- $\dfrac{\pi}{12}$
The value of $cos^{2}30^{0}-cos^{2}60^{0}-cos 60^{0}$ is
- $0$
- $\dfrac{1}{2}$
- $\dfrac{3}{4}$
- $1$
If $A+B=\dfrac { \pi }{ 3 } $ and $\cos { A } +\cos { B } =1 $, then which of the following are true:
- $\cos { \left( A-B \right) =\dfrac { 1 }{ 3 } } $
- $\cos { \left( A-B \right) =-\dfrac { 1 }{ 3 } } $
- $\left| \cos { A } -\cos { B } \right| =\sqrt { 2/3 } $
- $\left| \cos { A } -\cos { B } \right| =\cfrac { 1 }{ \sqrt { 3 } } $
The angle subtended at the centre of circle of radius $3$ metres by an arc of length $1$ metre is equal to
- $20^\circ $
- $60^\circ $
- $\dfrac{1}{3}\,radian$
- $\,3\,radian$
The value of $\dfrac{1}{\cos 290^o}+\dfrac{1}{\sqrt{3}\sin 250^o}$ is?
- $\dfrac{2\sqrt{3}}{3}$
- $\dfrac{4\sqrt{3}}{3}$
- $\sqrt{3}$
- None
Find the degree measure corresponding to $\left(\dfrac{1}{6}\right)^C$.
- $9.549^\circ$
- $9^032$ $43.6"$
- $10^0$
- None
If $\cos x=\sqrt{1-\sin2x},0\le x\le \pi$, then possible value of $x$ is
- $\pi$
- $0$
- $\tan^{-1}2$
- $3\pi$
The area of a sector of a circle of radius $7\ cm$ and central angle $120^{o}$ is
- $152\ cm^{2}$
- $\dfrac{154}{3}\ cm^{2}$
- $\dfrac{128}{3}\ cm^{2}$
- $128\ cm^{2}$
$\displaystyle \frac{\pi ^{c}}{5}$ in sexagesimal measure is _____
- $\displaystyle 18^{\circ}$
- $\displaystyle 36^{\circ}$
- $\displaystyle 54^{\circ}$
- $\displaystyle 72^{\circ}$
The value of $\displaystyle 144^{\circ}$ in circular measure is ___
- $\displaystyle \frac{3\pi ^{c}}{4}$
- $\displaystyle \frac{2\pi ^{c}}{3}$
- $\displaystyle \frac{4\pi ^{c}}{5}$
- $\displaystyle \frac{5\pi ^{c}}{6}$
Find the angle measure of $4$ radians.
- $114.591^{\circ}$
- $141.372^{\circ}$
- $229.183^{\circ}$
- $282.743^{\circ}$
- $458.366^{\circ}$
1 radian =
- $58^0.17$
- $65^0.17$
- $57^0.30$
- $66^0.71$
If $\displaystyle\cot \theta+\left ( \frac{1}{\sqrt{3}} \right )\sin \theta =\frac{2}{\sqrt{3}} $ then find $\displaystyle \theta $ in circular measure
- $\displaystyle \frac{\pi ^{2}}{2} $
- $\displaystyle \frac{\pi ^{2}}{3} $
- $\displaystyle \frac{\pi ^{2}}{4} $
- $\displaystyle \frac{\pi ^{2}}{6} $
The degree measure of 1 radian (taking $\pi =\dfrac { 22 }{ 7 }$ ) is
- $55^o{ 61 }^{ ' }{ 22 }^{ " }$ (approx.)
- $57^o{ 16 }^{ ' }{ 22 }^{ " }$ (approx.)
- $57^o{ 22 }^{ ' }{ 16 }^{ " }$ (approx.)
- $57^o{ 22 }^{ ' }{ 22 }^{ " }$ (approx.)
Convert $40^\circ ,20'$ into radian measure.
- $\dfrac {121}{540}\pi $ radians
- $\dfrac {121}{570}\pi $ radians
- $\dfrac {120}{513}\pi $ radians
- None
Find the radian measure corresponding to the degree $-47^{o}30'$
- $\dfrac {-19\ \pi}{72}rad$
- $\dfrac {19\ \pi}{72}rad$
- $\dfrac {13\ \pi}{72}rad$
- $None\ of\ these$