Download Government Polytechnic, Jamnagar General

Government Polytechnic, Jamnagar
General Department
Tutorial Exercise – 5 Trigonometry
1. Convert the following measurement of angle into radian:
i). 300 ii). 45 iii). 900 iv).1800 v). 7200
2. Convert the following measurement of angle into degree:
ii). 7πc/2
iii). πc/12
iv). 3πc/2
i). πc/8
3. Make the table for values of all trigonometric functions for angles
0, π/6, π/4, π/2, π, 3π/2,2π.
4. Find the value of
(i)
cos300 + sin2400 + tan600 + tan1200
(ii) cos2250 cos 6750 + sin 5850.sin 3150
5. Prove that sin 200 sin 400 sin 600 sin 800 =
6. Prove that
3
16
cos110 + sin110
= tan 560
0
0
cos11 − sin11
7. If sin (2A+B) = 5sinB then show that tan (A+B) =
3
tan A.
2
8. Prove that sin α i cos (β -α) + cosα i sin (β -α) = sin β.
9. Prove that 2 + 2 + 2 + 2 cos 8θ = 2 cos θ .
10.If tanA = 3, tanB = 2 find the value of tan(2A+B) and tan(A+2B).
1 + Sinα 1 − Sinα
= 2(Cosec2α - Cot α)
+
1 + cos α 1 − Cosα
π
3π
5π
7π
9π
=1
12. Prove that cot . cot . cot . cot . cot
20
20
20
20
20
11.Prove that
13. Prove that tan 3 A − tna 2 A − tan A = tan A tan 2 A tan 3 A
14. If tan −1 x + tan −1 y + tan −1 z = π , Prove that x + y + z = xyz.
1
1
1
1
3
5
7
8
3
15
36 π
16. Prove that sin −1 + cos −1 + sin −1 =
5
17
85 2
15.Prove that tan −1 + tan −1 + tan −1 + tan −1 =
π
4
17.Sketch graph of function (i) y = sin x (ii) y = cos x for the 0≤ x ≤ 2π
18.Find period of function (i) y = sin 5 x (ii) y = 4 cos(7 x + 3)
THE END.