Allied Angles

Q.

If, in two circles, arcs of the same length subtend angles ${60}^0$ and ${75}^0$ at the centre, find the ratio of their radii.

Q. If a line, OA(O is origin) makes an angle of ${30}^{\circ }$ with the negative x-axis, the angle it makes with the positive direction of x-axis is .

1. ${60}^{\circ }$
2. $-{150}^{\circ }$
3. ${120}^{\circ }$
4. ${150}^{\circ }$

Q. 5.Find the value of:(i) sin 75(ii) tan 15°

Q. If $\cos A=n\cos B$ and $\sin A=m\sin B$, then $(m^2-n^2){\sin }^{2}B=$

1. $1$
2. $1+n^2$
3. $n^2$
4. $1-n^2$

Q.

Find the slope of the line, which makes an angle of ${30}^{\circ }$ with the positive direction of y - axis measured anticlockwise.

Q.

Let the angle made by the line OA with respect to positive x-axis be ${\theta }_1$ and the angle made by OB be ${\theta }_2$. Find the value of ${\theta }_1+{\theta }_2(0\le |{\theta }_1|,|{\theta }_2|\le {180}^{\circ })$. Angle measured in clockwise direction is negative and angle measured in anti-clockwise direction is positive.

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Q.

The line OA makes an angle of $\theta ={30}^o$ with negative x-axis as shown in the figure. Which of the following could be the measure of the angle made by OA with respect to positive x-axis?

1. $-{30}^o$

2. $-{150}^o$

3. ${210}^o$

4. ${150}^o$

Q.

How many of the following statements are correct?

If AB and OC are straight lines and the angle made by OC with OB is ${30}^o$, then $\theta ={150}^o$

(2)

The angle made by OA with respect to positive x-axis is ${120}^{o}or-{240}^o$.

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Q. The value of ${\sin }^2\frac{\pi }{4}+{\sin }^2\frac{3\pi }{4}+{\sin }^2\frac{5\pi }{4}+{\sin }^2\frac{7\pi }{4}$ is

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

Q.

The line OA makes an angle of $\theta ={30}^o$ with negative x-axis as shown in the figure. Which of the following could be the measure of the angle made by OA with respect to positive x-axis?

1. -30^o

2. -150^o

3. 210^o

4. 150^o