INDIAN SCHOOL MUSCAT DEPARTMENT OF MATHEMATICS WORKSHEET ON TRIGONOMETRIC FUNCTIONS CLASS – XI (2017- 18) 1.
2.
3.
1 MARK QUES TIONS : Exp ress the following angles in radian measure : (i) 35 (ii) 3730 (iii) 4020 Find the degree measures for the follo wing : (i) 6 (ii) 3/4 (iii) -3 2 MARK QUES TIONS : Find the values of : (i) sin 1230
(ii)
tan 1590
(iii)
cos 870
(iv )
sin
19 4
(v)
4 tan 3
4.
The minute hand of a clock is 21cm long. How much distance does its tip move in 20 minutes ?
5.
Find the radius of the circle in which a central angle of 45 makes an arc of length 187 cm.
6.
Prove that : (i)
7.
2 sin 2
6
cos ec
7 2 29 cos2 0 (ii) 3 cos2 sec 5 tan 2 6 3 4 3 3 2
Find the principal solutions of the follo wing equations : (i)
1 3
tan x
(ii)
sec x 2
(iii)
sin x
3 2
4 MARK QUES TIONS : 8.
Prove that : (i) tan 50 tan 40 2 tan 10 (iii)
9. (i) If (ii) If 10.
cos 20 cos 40 cos 60 cos80
x y
4
, prove that
3 16
1 16
1 tan x1 tan y 2 tan x
If cos x 4 / 5 , cos y 12 / 13 , cos ( x + y ) and sin ( x - y ).
Show that (i)
sin 10 sin 50 sin 60 sin 70
m 1 and tan , show that m 1 2m 1 4
tan
11.
(ii)
2 sin sin 3
3 / 2 < x < 2 and 3 / 2 < y < 2 , find the values of
4 sin 3
0
(ii)
3 5 7 1 1 cos 1 cos 1 cos 1 cos 8 8 8 8 8
12. Find the value of 13.
tan
8
Prove the following : (i)
x 9x 7x cos x cos cos3x cos sin 4 x sin 2 2 2
(iii)
2 2 2 cos 4 x 2 cos x , 0 < x < π/4
sin 8x cos x sin 6 x cos 3x tan 2 x cos 2 x cos x sin 3x sin 4 x tan 5x tan 3x (iv) 4 cos 2 x cos 4 x tan 5x tan 3x cos x x (v) tan 1 sin x 4 2 (ii)
3 cos2 x cos2 x cos2 x 3 3 2 3 4 3 3 2 (vi) sin x sin x sin 3 x sin 3x 4 3 3 (v)
14.
Solve the following equations : (i) 4 sin x cos x 2 sin x 2 cos x 1 0
(ii) 3 tan x cot x 5 cos ecx
(iii) sin x 2 sin 2 x sin 3x cos x 2 cos 2 x cos 3x (iv ) (v)
tan 2 x 1 3 tan x 3 0
cot2 x 3 cos ecx 3 0
(vi) cos ecx 1 cot x
ANSWERS: Q1) 7 / 36 , 5 / 24 , 121 / 540 Q2) 3433811 , 425716 , 171495 Q3) ) ½, 1/√3, -√3/ 2, 1/√2, -√3 Q4) 44cm Q5)238cm Q7) (i)5π/6, 11π/6 (ii) 3π/4, 5π/4 (iii) 4π/3, 5π/3 Q10) 33/65, -16/65 Q12) √2-1 Q14) (i) x = 2nπ±2π/3; nπ+(-1)n 7π/6, nЄ Z (ii) x = 2nπ±π/3,nЄ Z (iii) x = 2nπ; nπ/2±π/8, nЄ Z (iv ) x = nπ+(-1)n (-π/2); nπ+(-1)n 7π/ 6
(v) x = nπ+π/4; nπ+π/3, nЄ Z
(vi) x = 2nπ+π/2,nЄ Z.
