Note: This is the Solution of review exercise 6.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 6.1
Question # 01: Find in which quadrant the following angles lie. Write a co-terminal angle for each:
\((i)\) \(\quad\) \( 65^\circ\)
\((ii)\) \(\quad\) \(135^\circ\)
\((iii)\) \(\quad\) \(-40^\circ \)
\((iv)\) \(\quad \)\(210^\circ \)
\((v)\) \(\quad \) \(-150^\circ \)
Question 2: Convert the following into degrees, minutes, and seconds:
\((i)\) \(\quad\) \( 123.456^\circ\)
\((ii)\) \(\quad\) \(58.7891^\circ\)
\((iii)\) \(\quad\) \(90.5678^\circ \)
Question 3: Convert the following into decimal degrees:
\((i)\) \(\quad\) \( 65^\circ{32}'{15}^{”}\)
\((i)\) \(\quad\) \( 42^\circ{18}'{45}^{”}\)
\((iii)\) \(\quad\) \( 78^\circ{45}'{36}^{”}\)
Question 4: Convert the following into radians:
\((i)\) \(\quad\) \( 36^\circ\)
\((ii)\) \(\quad\) \(22.5^\circ\)
\((iii)\) \(\quad\) \(67.5^\circ \)
Question 5: Convert the following into degrees:
\((i)\) \(\quad\) \( \frac{\pi}{16}\) rad
\((ii)\) \(\quad\) \( \frac{11\pi}{5}\) rad
\((iii)\) \(\quad\) \( \frac{7\pi}{6}\) rad
Question 6: Find the arc length and area of a sector if:
\((i)\) \(\quad\) \( r=6\) cm and central angle \(\frac{\pi}{3}\) radians
\((ii)\) \(\quad\) \( r=\frac{4.8}{\pi}\) cm and central angle \(\frac{5\pi}{6}\) radians
Question 7: If the central angle of a sector is \(\small{60^\circ}\) and the radius of the circle is the area of the secor and the percentage of the total area of the circle it represent.
Question 8: Find the percentage of the area of sector subtending an angle \(\small{\frac{\pi}{8}}\) radians.
Question 9: A circular sector of radius \(\small{r=12}\) cm has an angle \(\small{150^\circ}\). The sector is cut out and then bent to form a cone. What is the slant height and the radius of the base of this cone?
Hint: Arc length of secot = circumference of cone.
