More practice questions

5. Q5. Using π = 22/7, find the degree measures of (i) 11/16 radian; (ii) −4 radian (NCERT Exercise 3.1, Q2 (i), (ii)).

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   (i) (11/16) × 180 × 7/22 = 39.375° = 39° 22′ 30″. (ii) −4 × 180 × 7/22 = −(229 + 1/11) degrees; 1/11 degree = 60/11 = 5 + 5/11 minutes, and 5/11 minute = 300/11 ≈ 27.3 seconds, so −4 radian ≈ −229° 5′ 27″.

6. Q6. Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (use π = 22/7) (NCERT Exercise 3.1, Q4).

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   θ = l/r = 22/100 = 0.22 radian = 0.22 × 180 × 7/22 = 12.6° = 12° 36′.

7. Q7. In two circles, arcs of the same length subtend 60° and 75° at the centre. Find the ratio of the radii (NCERT Exercise 3.1, Q6).

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   With r₁ for 60° and r₂ for 75°, r₁θ₁ = r₂θ₂, so r₁ : r₂ = 75 : 60 = 5 : 4.

8. Q8. A pendulum 75 cm long swings so that its tip describes an arc of (i) 10 cm; (ii) 15 cm; (iii) 21 cm. Find the angle in radians each time (NCERT Exercise 3.1, Q7).

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   θ = l/75: (i) 10/75 = 2/15; (ii) 15/75 = 1/5; (iii) 21/75 = 7/25 radian.

9. Q9. Which angle between 0° and 360° ends in the same position as (i) 420°; (ii) −30°; (iii) −420°?

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   Add or subtract whole turns of 360°: (i) 420° − 360° = 60°; (ii) −30° + 360° = 330°; (iii) −420° + 720° = 300°.