Exercise 6.1 — Class 9 Mathematics Solutions

Find in which quadrant the following angles lie. Write a co-terminal angle for each.

${65}^{\circ }$

${135}^{\circ }$

$-{40}^{\circ }$

${210}^{\circ }$

$-{150}^{\circ }$

Convert the following into degrees, minutes and seconds.

${123.456}^{\circ }$

${58.7891}^{\circ }$

${90.5678}^{\circ }$

Convert the following into decimal degrees.

${65}^{\circ }{32}^{\prime }{15}^{\prime \prime }$

${42}^{\circ }{18}^{\prime }{45}^{\prime \prime }$

${78}^{\circ }{45}^{\prime }{36}^{\prime \prime }$

Convert the following into radian.

${36}^{\circ }$

${22.5}^{\circ }$

${67.5}^{\circ }$

Convert the following into degrees.

$\frac{\pi }{16}\text{rad}$

$\frac{11\pi }{5}\text{rad}$

$\frac{7\pi }{6}\text{rad}$

Find the arc length and area of a sector with:

$r=6$ cm and $\theta =\frac{\pi }{3}$ rad

$r=\frac{4.8}{\pi }$ cm and central angle $\theta =\frac{5\pi }{6}$ radians

If the central angle of a sector is ${60}^{\circ }$ and the radius of the circle is $12$ cm, find the area of the sector and the percentage of the total area of the circle it represents.

Find the percentage of the area of a sector subtending an angle of $\frac{\pi }{8}$ radians.

A circular sector of radius $r=12$ cm has an angle of ${150}^{\circ }$. This sector is cut out and then bent to form a cone. What is the slant height and radius of the base of the cone?

(Figure: a sector with centre $O$, both bounding radii $12$ cm and central angle ${150}^{\circ }$.)