Circular Measurement of Angle

Q.

Convert $95$ degrees Fahrenheit to degree Celsius.

Q.

If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Q. If the value of $\underset{x\to 0}{lim}(2-\cos x\sqrt{\cos 2x}{)}^{\left(\frac{x+2}{x^2}\right)}$ is equal to $e^a$, then $a$ is equal to

Q.

The value of expression $\frac{1}{\cos {290}^{\circ }}+\frac{1}{\sqrt{3}\sin {250}^{\circ }}$ is

1. $\frac{\sqrt{3}}{4}$

2. $\frac{4}{\sqrt{3}}$

3. $\frac{2}{\sqrt{3}}$

4. $\frac{\sqrt{3}}{2}$

Q. Find the principal solutions of the equation $\tan x=-\frac{1}{\sqrt{3}}.$

Q.

$Thedomainof\sqrt{sin\left(cosx\right)}$

1. 

2. 

3. 

4. 

Q. If the complete solution set of the inequality $({\text{cosec}}^{-1}x{)}^2-2{\text{cosec}}^{-1}x\ge \frac{\pi }{6}({\text{cosec}}^{-1}x-2)$ is $(-\infty ,m]\cup [n,\infty )$ , then $(m+n)$ is

Q.

How do you define one radian?

Q.

If $\sin \left(\theta \right)=-\frac{1}{\sqrt{2}}$ and $\tan \left(\theta \right)=1$, then $\left(\theta \right)$ lies in which quadrant $?$

1. First

2. Second

3. Third

4. Fourth

Q.

What is the superlative degree of bad?

Q.

How many radians is $2\mathrm{\pi }$?

Q.

${\cos }^{-1}\left(\frac{1}{2}\right)+2{\sin }^{-1}\left(\frac{1}{2}\right)$ is equal to

1. $\frac{\mathrm{\pi }}{4}$

2. $\frac{\mathrm{\pi }}{6}$

3. $\frac{\mathrm{\pi }}{3}$

4. $\frac{2\mathrm{\pi }}{3}$

Q. If both $\theta$ and $\varphi$ are acute angles such that $\sin \theta =\frac{1}{2}$ and $\cos \varphi =\frac{1}{3}$, then $(\theta +\varphi )$ belongs to

1. $(\frac{\pi }{3},\frac{5\pi }{12})$
2. $(\frac{\pi }{2},\frac{2\pi }{3})$
3. $(\frac{2\pi }{3},\frac{5\pi }{6})$
4. $(\frac{5\pi }{12},\frac{\pi }{2})$

Q.

How do you evaluate $\sec \left(150°\right)$ ?

Q.

A vertical stick $20m$ long casts a shadow $10m$ long on the ground,

At the same time a tower casts a shadow $50m$ long on the ground, the height of the tower is?

1. $25m$

2. $100m$

3. $120m$

4. $200m$

Q.

At 3:40, the hour and minute hands of a clock are inclined at

1. $\frac{7{\pi }^c}{12}$

2. $\frac{2{\pi }^c}{3}$

3. $\frac{13{\pi }^c}{18}$

4. $\frac{3{\pi }^c}{4}$

Q. The value of $\left\{\sin \frac{25\pi }{3}\right\}$ is
(where $\{.\}$ is fractional part function)

1. $0$
2. $\frac{1}{2}$
3. $\frac{\sqrt{3}}{2}$
4. $\frac{1}{\sqrt{2}}$

Q. The value of $\frac{\cos {58}^{\circ }}{\sin {32}^{\circ }}+\frac{\sin {22}^{\circ }}{\cos {68}^{\circ }}-\frac{\cos {38}^{\circ }\text{cosec}{52}^{\circ }}{\tan {18}^{\circ }\tan {35}^{\circ }\tan {72}^{\circ }\tan {55}^{\circ }}$
is

1. $\frac{1}{2}$
2. $1$
3. $2$
4. $0$

Q.

How do you find the degree measure of an angle $?$

Q.

Find the exact value of $\tan \frac{\mathrm{\pi }}{3}$.

Q.

If ${\tan }^2\alpha {\tan }^2\beta +{\tan }^2\beta {\tan }^2\gamma +{\tan }^2\gamma {\tan }^2\alpha +2{\tan }^2\alpha {\tan }^2\beta {\tan }^2\gamma =1$, then the value of ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma$ is

1. $0$

2. $-1$

3. $1$

4. None of these

Q.

How many degrees equals $1$ radian?

Q.

The value of the expression $\left[\text{cosec(75°+θ)-sec(15°-θ)-tan(55°+θ)+cot(35°-θ)}\right]$ is

1. $-1$

2. $0$

3. $1$

4. $32$

Q.

Find the value of $\sin {75}^{\circ }$using sum or difference identity.

Q.

The value of $\tan \left(\frac{\mathrm{\pi }}{5}\right)+2\tan \left(\frac{2\mathrm{\pi }}{5}\right)+4\cot \left(\frac{4\mathrm{\pi }}{5}\right)$ is

1. $\cot \left(\frac{\mathrm{\pi }}{5}\right)$

2. $\cot \left(\frac{2\mathrm{\pi }}{5}\right)$

3. $\cot \left(\frac{4\mathrm{\pi }}{5}\right)$

4. $\cot \left(\frac{3\mathrm{\pi }}{5}\right)$

Q. If $\tan \theta =-\frac{4}{3}$ and $\theta$ does not lie in the second quadrant, so the value of $\sin \theta$ is

1. $-\frac{4}{5}$
2. $\frac{4}{5}$
3. $\pm \frac{4}{5}$
4. $\pm \frac{3}{5}$

Q.

Value of ${\tan }^{-1}\left[\frac{\sin \left(2\right)-1}{\cos \left(2\right)}\right]$ is

1. $\left(\frac{\mathrm{\pi }}{2}\right)-1$

2. $1-\left(\frac{\mathrm{\pi }}{4}\right)$

3. $2-\left(\frac{\mathrm{\pi }}{2}\right)$

4. $\left(\frac{\mathrm{\pi }}{4}\right)-1$

Q. $\text{If}\alpha ,\beta ,\gamma$ are the angles which a line makes with the positive directions of coordinate axes, then ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma$ is equal to

1. $1$
2. $2$
3. $3$
4. $4$

Q. If $\sin {21}^{\circ }=\frac{x}{y}$, then $\sec {21}^{\circ }-\sin {69}^{\circ }$ is equal to

1. $\frac{x^2}{y\sqrt{y^2-x^2}}$
2. $\frac{y^2}{x\sqrt{y^2-x^2}}$
3. $\frac{x^2}{y\sqrt{x^2-y^2}}$
4. $\frac{y^2}{x\sqrt{x^2-y^2}}$

Q. If $\sin x=\frac{3}{5},\cos y=-\frac{12}{13}$, where $x$ and $y$ both lie in second quadrant, find the value of $\sin (x+y)$.