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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.