Worksheet on Trigonometric Angles

Practice the questions given in the worksheet on trigonometric angles to know the origin, development and necessity of trigonometry, different methods for measuring trigonometric angles, differentiate between trigonometric and geometric angles.

1. Express in degrees, minutes and seconds:

(i) 832’

(ii) 7312”

(iii) 375”

(iv) 271/12

(v) 72.04°

2. Find the circular measures:

(i) 60°

(ii) 135°

(iii) -150°

(iv) 27°

(v) 22° 30’

(vi) -67° 30’

(vii) 52° 52’ 30”

3. In a triangle one of the angles is 65° and the second one is π /12 find the sexagesimal and circular measures of the third angle.

4. The radius of a circle is 7 cm. Find the circular measure of the angle at the centre by an arc of this circle 5.5 cm in length.

5.The sum and difference of two angles are 135° and π /12 respectively. Find the sexagesimal and circular measures of the angles.

6. A rotating ray traces angle -5 π/12. State, in what direction the ray moves, and find how many complete revolutions it makes and how much more in degrees the ray rotates.

7. In an isosceles triangle ABC, ∠ABC contained by two equal side measures 45°. The bisector of ∠ABC meets AC at the point D. Find the circular measures of ∠ABD, ∠BAD, ∠CBD and ∠BCD.

8. ∠ABC of a right-angled triangle ABC is 90° and ∠BAC = 3 π/8. The perpendicular from the point B on AC meets AC at the point D. Mention the names of all the angles of ∆ABD and ∆BCD and write down their circular measures.

9. Produce the base BC of an equilateral triangle ABC to the point E, such that CE = BC. Join A, E. Now mention the names of all the angles of ∆ACE and write down their circular measure&

10. If π/3, 5π/6 and 90° be any three angles of a quadrilateral, find the fourth angle in terms of sexagesimal and circular systems.

Answers for the worksheet on trigonometric angles are given below to check the exact answers of the above question.


1. (i) 13° 52’

(ii) 2° 1’ 52”

(iii) 6’ 15”

(iv) 27° 5’

(v) 72° 2’ 24”

2. (i) π/3

(ii) 3 π/4

(iii) -5 π/6

(iv) 3 π/20

(v) π/8

(vi) -3 π/8

(vii) 47 π/160

3. 100°, 5π/9

4. π/4

5. 75°, 60° and 5π/12, π/3

6. 2 complete revolutions and 195° clockwise

7. ∠BAD = ∠BCD = 3π/8, ∠ABD = ∠CBD = π/8

8. ∠BAD = ∠DBC = 3π/8; ∠ABD = ∠BCD = π/8 and ∠ADB = ∠BDC = π/2

9. ∠EAC = ∠AEC = π/6; ∠ACE = 2π/3

10. 60°, π/3

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