Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Trigonometry - Arc lengths and sectors.
Test Yourself 1 - Solutions.


 

Arc length. 1.
  2.
  3.
  4.
  5. (i)

(ii)

  6.
Find angle. 7.
  8.
Find radius. 9. 35 = 2.3 r

r = 15.22 cm.

  10. 98° = 1.71 radians.

∴ 42 = r × 1.71

r = 24.6 cm.
  11.
Miscellaneous. 12. (i)

(ii)

  13. (i)

(ii)

The point P is therefore (40 + 32) = 72 cm above the path.
Area of a sector 14.
  15. (i)

(ii)

  16. (i)

(ii) To find the area of △ ADB, need AD:

 

17.

  18.
  19. (i)

(ii)

  20. (i) To find the radius of the arc:

An equilateral triangle has all angles = 60°.
The vertical line from the apex = radius = 6 cm.

(ii) Find the area of the shaded portion in exact form.
Mixed exercises.

21.

  22. (i)

(ii)

(or use radian mode in your calculator).
  23. (i)

(ii) Arc length = 6 × 1.5 = 9 cm.
  24. (i)

(ii)

  25. (i)

(ii)