Karnataka 1st PUC Mathematics Trigonometric Functions MCQ with Answers

GOVERNMENT OF KARNATAKA
DEPARTMENT OF SCHOOL EDUCATION (PRE-UNIVERSITY)
TH
18 CROSS, MALLESHWARAM, BENGALURU – 560 012
CHAPTERWISE MULTIPLE CHOICE QUESTIONS FOR COMPETATIVE EXAM
SUBJECT: MATHEMATICS – I PUC
NAME OF THE CHAPTER: TRIGONOMETRIC FUNCTIONS

ANGLES AND THEIR MEASURES
Angle
A figure traced by rotating a given ray about its end point. The measure of angle is the amount of rotation
performed from the initial side to the terminal side. Angle performed by anticlockwise rotation are taken as
positive whereas angles formed by clockwise rotation are considered as negative.

Radian or Circular Measure
The angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the radius of

the circle is called 1 radian and is denoted by 1c.
When no unit is mentioned with an angle, it is always understood to be in radian.
Radian measure and real numbers are same.
The ratio of circumference and diameter of a circle is always constant and denoted by Greek letter '  '.
Circumference of Circle
 is an irrational number, π =
Diameter of Circle
22
Circumference = 2  r =  × diameter, π = (approx) = 3.1415........
7

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Arc-angle relation
arc l
Angle  , θ = Here angle is always in radian.
radius r
Chord AB
Angle subtended by a very small arc is approximately calculated by θ =
r
Arc AB  chord AB for small angle 
Relation between degree and radian.

  
0 c

  180 , 1  
180 
 , 1 
c 0 c 0

    180 
Relation between the sides and interior angles of a polygon

(a) Sum of interior angle of polygon of n sides = (2n – 4) × 90° = (n – 2) c

 2n  4  900   n  2   c
(b) Each interior angle of a regular polygon of n sides =
n n
Graphs of Trigonometric Functions with domain and range

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Trigonometric Ratios Of Allied Angles

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
T-ratios of  
   in terms of  for all values of  :
2 
    sin  , if n is even
 sin  n.     
 2   cos  , if n is odd
    cos  , if n is even
 cos  n.     
 2   sin  , if n is odd

    tan  , if n is even
 tan  n.     
 2   cot  , if n is odd
    cot  , if n is even
 cot  n.     
 2   tan  , if n is odd
    sec  , if n is even
 sec  n.     
 2   cos ec , if n is odd

    cos ec , if n is even
 cos ec  n.     
 2   sec  , if n is odd
Points to remember
o
11
 The angle b/n hour hand and minute hand when the time is A hour B minutes is given by 30A - B
2
Formulae for the trigonometric ratios of sum and differences of two angles
 sin  A  B  sinA.cosB  cosA.sinB

 sin( A  B)  sin A cos B  cos A sin B
 cos( A  B)  cos A cos B  sin A sin B
 cos( A  B)  cos A cos B  sin A sin B
tan A  tan B
 tan( A  B) 
1  tan A tan B
tan A  tan B
 tan( A  B) 
1  tan A tan B
cot A cot B  1
 cot( A  B) 
cot A  cot B
cot A cot B  1
 cot( A  B) 
cot B  cot A
 sin( A  B)sin( A  B)  sin A  sin B  cos B  cos A
2 2 2 2

 cos( A  B) cos( A  B)  cos A  sin B  cos B  sin A
2 2 2 2

 tanA  tanB  tan  A  B tanAtanB  tan(A  B)

1  tan θ 1  tan θ
 tan  450  θ   ; tan  45 0  θ  
1  tan θ 1  tan θ

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Trigonometric ratios of multiple angle :-
2 tan A
 sin 2 A  2sin A cos A 
1  tan 2 A
1  tan 2 A 
 cos 2 A  2 cos A  1  1  2sin A  cos A  sin A 
2 2 2 2
; where A  (2n  1) .
1  tan A
2
4
2 tan A
 tan 2 A 
1  tan 2 A
Trigonometric ratios of multiple angle :-
 sin 3 A  3sin A  4sin 3 A
 cos 3 A  4 cos3 A  3cos A
3 tan A  tan 3 A
 tan 3 A  , where A  n   / 6 A  n   / 6
1  3 tan 2 A
Complimentary angles
 A & B are said to be complimentary if A + B =
 sin A = cos B, tan A = cot B, cosec A = sec B Where A & B are complimentary angles
 If are complementary angles, and

 ( )

Trigonometric ratios of half angles:-

θ
2tan  
θ θ 2
sinθ = 2sin   .cos   =
2  2  1 + tan 2  θ 
 
2
θ
2tan  
tanθ = 2
θ
1 - tan 2  
2
θ
1 - tan 2  
θ θ θ θ 2
cosθ = cos 2   - sin 2   = 2cos 2   - 1 = 1 - 2sin 2   =
2 2 2  2  1 + tan 2  θ 
 
2
Some Important Formulae
1  cos A  A 
  tan  
sin A 2 1  cos 2 A  2 cos A

1  cos A  A
  cot    1  cos 2 A  2 s inA
sin A 2
 1  sin 2 A  cos A  sin A

 1  sin 2 A  cos A  sin A

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 Transformation formulae:-
 2sin A cos B  sin( A  B)  sin( A  B)
 2 cos A sin B  sin( A  B)  sin( A  B)
 2 cos A cos B  cos( A  B)  cos( A  B)
 2sin A sin B  cos( A  B)  cos( A  B)
CD CD
 sin C  sin D  2sin cos
2 2
CD CD
 sin C  sin D  2 cos sin
2 2
CD CD
 cos C  cos D  2 cos cos
2 2
CD D C CD CD
 cos C  cos D  2sin sin  2sin sin .
2 2 2 2
 If then
☻
☻
☻
☻
 Important results:-

⃰ If √ then
√

⃰ ( )

⃰
⃰
⃰
⃰
⃰ If , then

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Multiple choice questions:
1. If in two circles, arcs of the same length subtend angles 30 and 78 at the centre, then the ratio of
their radii is Easy (KCET 2024)

1) 2) 3) 4)

2. The angle between hour hand and minute hand of a clock when the time is 5 hours 20 minutes
Difficult
1) 2) 3) 4)
3. The degree measure of is equal to Average (KCET 2022)

1) 5 30 20” 2) 5 37’30” 3) 5 37’20” 4) 4 30’30”

4. If for real values of x, , then Easy

1) is an acute angle 2) is right angle
3) is an obtuse angle 4) No value of is possible
5. In triangle angle then Easy
1) 1 2) 3) 0 4) 1
6. The minimum value of 1 – sin x is Average (KCET 2025)
1) 2 2) 0 3) – 1 4) 1
7. If ABC is right angled at C, then the value of tan A + tan B is Difficult (KCET 2024)

1) a + b 2) 3) 4)
8. Which of the following is not correct? Easy

1) 2) 3) 4)
9. Which of the following is correct? Average
1) 2) 3) 4)

10. If tan θ + cot θ = 2, then what is the value of tan100 θ + cot100 θ Average
1) 2) 3) 4)
11. If sin x  sin 2 x  sin 3 x  1 , then cos 6 x  4 cos 4 x  8cos 2 x = Difficult
1) 3 2) 4 3) 2 4) 1
12. If A lies in the second quadrant and 3tanA + 4 = 0 then the value of 2cotA  5cosA  sinA
is equal to Average

1) 2) 3) 4)

13. If then sin is Easy

1) but not 2) or 3) but not 4) None of these

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4
14. If sinθ   and lies in third quadrant then the value of is Difficult
5

1) 2) 3) 4)
√ √ √

15. The maximum value of sin(x + /6) + cos(x + /6) is attained at x = Average (KCET 2026)
1) /2 2) /4 3) /6 4) /12
16. The value of is Easy (KCET 2021)

1) 0 2) 1 3) 4) Not defined
17. log tan1 0 + log tan 2 0 + log tan 3 0 + ………………….. + log tan 89 0 = Average
1) 2) 3) 1 4)
18. The value of + is equal to Easy
1) 1 2) 180 3) 0 4) -1
( )
19. Average

1) e 2) 0 3) 4) 1
20. Which of the following is not correct? Average (KCET 2025)
1) tan45° = tan (– 315°) 2) cos5 = cos4
3) sin2 = sin (– 2 ) 4) sin4 = sin6
21. The value of cos1200° + tan1485° is Difficult (KCET 2021)

1) 2) 3) 4)
22. The value of tan15 0 + cot 15 0 = Average
1) 1 2) √ 3) 4 4) √
cot72° tan18°
23. + = Average
tan18° cot72°
1) 1 2) 0 3) 2 4) 3
24. The value of tan ( ) + tan ( ) is : Difficult

1) 2) 3) 4)
( ) ( ) ( ) ( )

25. The value of sin25 0 + sin210 0 + sin215 0 + ……………… + sin290 0 = Difficult
1) 8 2) 9 3) 7 4) 9 ½

26. The value of ( ) ( ) is Average

1) 1 2) 0 3)1 4) Not defined

27. The value of  sin 2  2k 0  is
45
Difficult
k 1

1) 23.5 2) 23 3) 45 4) 0

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28. The value of ( ) ( ) is Average
1) 2) 3) 1 4) 0
29. ( ) ( ) is equal to Difficult
1) ( ) 2) ( ) 3) ( ) 4) ( )
30. What will be the value of sec 4 θ - tan4 θ, if sec 2 θ + tan2 θ = . Average
1) 2) 3) 1 4)
31. If then is equal to Average
1) 1 2) 4 3) 2 4) None of these
32. If cos x + x = 1, then the value of x+ x is Easy (KCET 2025)
1)2 2) –1 3)1 4) 0
33. If , what is the largest angle of a triangle whose sides are Average

1) 2) 3) 4)

34. If ( ) then Average
1) ( ) 2) ( ) 3) ( ) 4) ( )

35. The value of 3  sinA  cosA   6  sinA  cosA   4  sin 6 A  cos6 A  is
4 2
Difficult

1) 12 2) 13 3) 14 4) 15

36. √ √ √ = Average (KCET 2022)

1) sin 2 2) 2sin 3) 2cos 4) 2 cos

37. If and then the value of ( ) is Easy

1) 2) 3) 0 4)

38. If then the value of ( )( ) is Average

1) 1 2) 2 3) 2 4) Not defined
39. If then is equal to Difficult

1) a 2)b 3) 4) None of these

40. If , then is equal to Difficult

1) 2) 3) 4)
sinx
41. = Average
x
sin  
8
x x x x x x x x x x x x
1) 8cos sin cos 2) 8cos cos sin 3) 8cos cos cos 4) 8sin sin sin
8 4 2 8 4 2 8 4 2 8 4 2

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42. The value of is Difficult (KCET 2022)

1) 0 2) 3) 1 4)

43. The value of is equal to Easy
1) 2)
3) tanAtan2A tan2Atan3A 
tan3AtanA 4) None of these
44. tan A+tan 2A+tan3Atan 2AtanA= Average
1) 2 tan 2A 2) 3 tan A 3) tan 3A 4) tan 5A
45. If (1 + tan A) (1 + tan B) = 2 then A + B = Average
1) 300 2) 450 3) 900 4) 00
46. The value of tan20 0 + tan 40 0 + √ tan20 0 Tan40 0 = Average
√ √
1) √ 2) 3) 4) none of these

47. √ Difficult
1) 4 2) 2 3) 1 4) 3

48. The value of is Easy

√
1) 1 2) √ 3) 4) 2
49. What is the value of (2tan 15 0) / (1 + tan2 15 0) Easy
√
1) 2) 2 3) 4) 1

50. If √ then is Difficult

1) 2) 3) 4)
√
51. If , then the least positive value of x is Difficult
√

1) 2) 3) 4)
n
52. f x   f x is
sin 6 x
,x  then the range of the function Difficult
sin 2 x 2
1) [-1,1] 2) [-1 , 3) 3) [-1,3] 4) (-1,3)
53. The value of is equal to Difficult

1) √ 2) √ 3) 4)
√

Hint: Use the formula

54. The value of sin200 sin400 sin600 sin800 is Difficult

1) 2) 3) 4)

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1
55. If sinx - siny = and cosx - cosy = 1 then ( ) Difficult
2

1) 2) 3) 4)

56. The value of sin 500  sin 700  sin100 is equal to Average

1) 1 2) 3) 4) 2

sin700 + cos400
57. = Average
cos700 + sin400

1) 1 2)√ 3) 4)
√
2 12 10 8 6
58. If sinx + sin x = 1 then cos x +3 cos x + 3 cos x + cos x = Difficult
1) 2) 3) 4) .
59. The domain of the function √ is Easy
 3π   π  π π  π   3π 
1)  , 2π  2)  0,  3)   ,  4)  0,    ,2 π 
2   2  2 2  2  2 
 13
60. The value of sin sin is Difficult
10 10

1) 2) 3) 4) 1

TRIGONOMETRIC FUNCTIONS
1 2 3 4 5 6 7 8 9 10
2 2 2 4 4 2 3 3 2 1
11 12 13 14 15 16 17 18 19 20
2 2 2 3 4 2 2 3 4 2
21 22 23 24 25 26 27 28 29 30
1 3 3 2 4 3 2 4 2 4
31 32 33 34 35 36 37 38 39 40
3 3 4 4 2 3 4 2 2 2
41 42 43 44 45 46 47 48 49 50
3 4 1 3 2 1 1 3 3 4
51 52 53 54 55 56 57 58 59 60
2 2 4 3 3 2 2 1 4 3

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Additional Questions
1. The angle subtended at the centre of a circle of radius 3metres by an arc of length 1metre is equal to
Easy
1)20° 2) 60° 3) 1/3 radian 4) 3 radians.
2. Two different arcs of same length of two circles subtend 300 and 450 at the centre of the two circles.
Then the areas of the two circles are in the ratio Average
1) 4 : 9 2) 9 : 4 3) 3 : 2 4) 2 : 3
3. The value of ( )( ) Easy
1) 2 2) √ 3) 1 4) 1/ √
4. If are complementary angle then Easy
1) 2) 1 3) 4) 2
5. The angles of a triangle are in A.P and the greatest angle is double the least angle, 'then sine of the
third angle is Average (KCET 2026)
√
1) 2) 3) 4) 0
√

6. If and lies in third quadrant , then the value of is Easy

1) 2) 3) 4)
√ √ √ √
7. If A is in the quadrant, then 5sin 2 A  3sin A  4cos A  Average

1) 0 2) 3) 4)

8. If tan x = , , then the value of is Average

1) 2) 3) 4)
√ √ √ √

9. The value of is Easy

1) 2) 0 3) 1 4) 1
√
10. cos1 0 + cos20 + cos3 0 + ……………………… cos 1800 = Average
1) 2) 3) 2 4)
0 0 0 0
11. The value of elog10tan1 +log10tan2 +log10tan3 +…………..+log10tan89 is Average (KCET 2023)

1) 1 2) 0 3) 4) 3

12. Average

1) 2) 1 3) 4) .
√

13. = Average

1) 1 2) 0 3) 2 4) 3

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14. ( ) ( ) Easy

1) 2) 3) 4)
15. If sinx + sin2x = 1 then cos 2x + cos4x = Easy
1) 2) 3) 4)
16. If , then the value of is equal to Easy

1) 1 2) 3) 0 4) 1

17. If , then ( ) is equal to Difficult
1) 1 2) 2 3) 3 4) 4

18. If tan A = then tan 2A = Average

1) tan 2) tan B 3) tan 2B 4) none of these

19. The value of is Difficult
√ √ √ √
1) 2) 3) 4)
√
0 0 0 0
20. tan 25 tan20 + tan25 + tan20 = Difficult
1) 2) 3) 4)
Additional Questions
1 2 3 4 5 6 7 8 9 10
3 2 1 2 1 3 1 4 2 4
11 12 13 14 15 16 17 18 19 20
1 2 3 2 1 3 3 2 1 2

Analytical Thinking MCQs
1. The value of the product is equal to
√
1) √ 2) 3) 3 4) 1

2. If , then the value of ( ) ( ) is equal to

1) 2) 3) 4)

3. If ( ) , where is a constant, then the value of is equal to
1) 12 2) -8 3) -4 4) 8
4. If and are real constants such that , then the value of

( ) ( ) is equal to
1) √ 2) √ 3) √ 4) √

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5. If , then the value of is equal to

1) 2) 3) 4)

6. If and , then the value of is

1) 2) 3) 4)

7.
√ √ √ √
1) 2) 3) 4)

8. The value of ( ) ( ) is equal to

1) √ 2) √ 3) √ 4) √
9. If , then lies
1) only in the first quadrant 2) only in the second quadrant
3) in the first quadrant or in the fourth quadrant 4) in the first quadrant or in the third quadrant
10. If ( √ ) √ and , then the values of are
1) 2) 3) 4)

11. If and , where then

1) 2) 3) 4)

12. The value of is equal to

1) ( ) 3) ( )

3) ( ) 4) ( )

13. The value of ( ) ( ) is equal to
1) 8 2) √ 3) -2 4) -8

14. ( ) ( ) ( ) ( )

1) √ 2) √ 3) √ 4) √

15. ( ) ( ) ( ) ( ) ( ) is equal to

1) 2) 3) 4)
16. The value of is equal to

1) ( ) 2) 0

3) ( ) 4)

17. Let be an arc of a circle which subtends at the centre. If the radius of circle is 4 , then the
length of the in centimeter is
1) 2) 3) 4)
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18. If ( ) then the value of is

1) 2) 3) 4)

19. If , then is equal to

1) √ 2) √ 3) √ 4) √

√ ( )
20. The value of is

1) 1 2) √ 3) √ 4)

21. If , then is equal to

1) 1 2) √ 3) √ 4) √

22. The value of is equal to

1) 2) √ 3) 1 4) √
√

23. The value of is equal to
1) 1 2) 2 3) √ 4) 2
24. Let ( ) ( ) . Then the maximum value of is
1) 325 2) 365 3) 385 4) 430
25. Consider the following statements:
1. cos  sin  can never be equal to 1.5 2. tan   cot  can never be less than 2
Which of the above stateme nts is/are correct?
1) 1 only 2) 2 only 3) Both 1 & 2 4) Nether 1 nor 2
26. Express 50037 '30'' in radian
7 5 9 
1) 2) 3) 4)
32 32 32 32

1 - sinθ 1 + cosθ  =
27.
1 - cosθ 1 + sinθ 
1)  sec  tan   cos ec  cot   2)  sec  tan   cos ec  cot  

3)  sec  tan   cos ec  cot   4)  sec  tan   cos ec  cot  

12  
28. If     , 0  and cos    , then sin   
13 2

5 26 5 26 5 13 5 13
1)  2) 3)  4)
26 26 13 13

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29. Match the exact values of the trigonometric ratios in Column I with the constants in Column II
Column I: Column II:

A. sin180 p. 2  3

5 1
B. cos 360 q.
4

5 1
C. tan150 r.
4
1) A  q, B  r, C  p 2) A  r, B  q, C  p
3) A  q, B  p, C  r 4) A  p, B  q, C  r
30. Identify which of the following graph is cos 2x

Analytical Thinking MCQs
1 2 3 4 5 6 7 8 9 10
4 4 2 1 3 1 3 1 4 3
11 12 13 14 15 16 17 18 19 20
4 1 3 1 2 2 2 3 3 1
21 22 23 24 25 26 27 28 29 30
4 1 1 3 1 3 2 1 1 3

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