Standard Angles

Q. Given:
$sin(B+C)=\frac{\sqrt{3}}{2}$
$sin(A+C)=sinB\text{and}$
$sinA=\frac{1}{2}.$

$\text{Find the value of}sin(A+B-C)?$

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

Q.

$2ta{n}^2{45}^{\circ }+3co{s}^2{30}^{\circ }-si{n}^2{60}^{\circ }=$___

1. $\frac{7}{2}$

2. $\frac{2}{7}$

3. $\frac{17}{2}$

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

Q.

We can cut out a triangle of side 8 cm whose opposite angle is ${30}^{\circ }$ from a circular sheet of diameter $16cm[sin{30}^{\circ }=0.5]$

1. True

2. False

Q. Find the acute angle $\left(\theta \right)$ at which
$sin\theta andtan\theta \text{are equal?}$

1. ${45}^{\circ }$
2. ${90}^{\circ }$
3. $0^{\circ }$
4. ${30}^{\circ }$

Q.

Arjun saw an equation written like $4sin2\theta =5$. Can you suggest Arjun whether the given equation is true or false?

1. True

2. False

Q.

Find the value of $\frac{1-ta{n}^2{30}^o}{1+ta{n}^2{30}^o}$.

1. 2

2. 0.5

3. 4

4. 1

Q. If $sin(B+C)=\frac{\sqrt{3}}{2}$, $sin(A+C)=sinB\text{and}$ $sinA=\frac{1}{2}.$, then $\sin (A+B-C)$ is .

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

Q.

If $\cos 3\theta =\frac{\sqrt{3}}{2};0<\theta <200$, then the value of $\theta$ is:

1. 12 degrees

2. 15 degrees

3. 10 degrees

4. 0 degrees

Q.

A kite is attached to a string. Find the length of the string, when the height of the kite is 60 m. and the string makes an angle ${30}^{\circ }$ with the ground. [2 MARKS]

Q. Taking $\theta ={30}^{\circ }$, verify that:

$\left(i\right)sin3\theta =3sin\theta -4si{n}^3\theta$

$\left(ii\right)cos3\theta =4co{s}^3\theta -3cos\theta$ [2 MARKS]

Q. Find the value of $\frac{\cos {30}^o\tan {60}^o+\sin {60}^o\cos {60}^o}{cosec{30}^o\sec {60}^o-cosec{60}^o\cot {30}^o}$

Q.

cos$1^{\circ }$ $\times$ cos$2^{\circ }$ $\times$ cos$3^{\circ }$ $\times$……..$\times$ cos ${180}^{\circ }$ is equal to ____.

1. $\frac{1}{2}$

2. 0

3. 1

4. -1

Q. If $\cos 3\theta =\frac{\sqrt{3}}{2}$, $0°<3\theta <90°$, the value of $\theta$ (in degrees) is

1. 10

Q. If $sin(B+C)=\frac{\sqrt{3}}{2}$, $sin(A+C)=sinB\text{and}$ $sinA=\frac{1}{2}.$, then $\sin (A+B-C)$ is .

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

Q. If $sin(B+C)=\frac{\sqrt{3}}{2}$, $sin(A+C)=sinB\text{and}$ $sinA=\frac{1}{2}.$, then $\sin (A+B-C)$ is .

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

Q. If $sin(B+C)=\frac{\sqrt{3}}{2}$, $sin(A+C)=sinB\text{and}$ $sinA=\frac{1}{2}.$, then $\sin (A+B-C)$ is .

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

Q. Find the value of
$sin\theta +cos\theta \text{, when}\theta ={45}^{\circ }$

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

Q.

For what value of A is sin A = cos A?

1. 0°

2. 30°

3. 90°

4. 45°

Q.

The value of expression $tan\theta -cot\theta at\theta ={30}^{\circ }$ is 1.

1. False
2. True

Q. $Findthevalueofsi{n}^2\theta +co{s}^2\theta at\theta ={30}^{\circ }\&{60}^{\circ }$.

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

Q.

$Ifsin(B+C)=\frac{\sqrt{3}}{2}andsinA=\frac{1}{2}$, find $B+CandA$.

1. $B+C={60}^{\circ }andA={30}^{\circ }$

2. $B+C={30}^{\circ }andA={30}^{\circ }$

3. $B+C={45}^{\circ }andA={60}^{\circ }$

4. $B+C={60}^{\circ }andA={60}^{\circ }$

Q. If $\theta$ is any acute angle, what is the area of a square with adjacent sides $sin\theta$ and $cosec\theta$?

1. 0
2. $sin\theta \times cos\theta$
3. $co{s}^2\theta$
4. $si{n}^2\theta$