Exam (elaborations) Trigonometry

Subject:-Mathematics
Topic:-Trigonometric MCQ
Level:-All Entrances Exams
1. What is the measure of the angle 1140 35′ 30′′ in radian?

a) 1 rad b) 2 rad

c) 3rad d) 4rad

A. The answer is b) 2rad
1 ′ 71 ′
soln:- 35′ 30′′ = (35 + ) = ( )
2 2

71 ′ 71 1 0 71 0
⇨( ) =( × ) =( )
2 2 60 120


0 ′
71 0
′′
13751 0
∴ 114 35 30 = (114 + ) =( )
120 120
We know that , 2𝜋 𝑟𝑎𝑑 = 3600
13751 0 2𝜋 13751
⇨( ) = 3600 × = 2.00008069 𝑟𝑎𝑑 = 2 𝑟𝑎𝑑 (𝑎𝑝𝑝𝑟𝑜𝑥).
120 120




10
2. What is the value of sin 292 ?
2

1 1
a) √2 + √3 b) − √2 − √3
3 3

1 1
c) √2 + √2 d) − √2 + √2
2 2

1
A. The answer is d) − √2 + √2
2

10 585 0
soln:- sin (292 ) = sin ( )
2 2

, 1
(1−𝑐𝑜𝑠5850 ) 1−𝑐𝑜𝑠2250 1+𝑐𝑜𝑠450 (1+ )
= −√ = −√ = −√ = −√ √2
2 2 2 2


√2+1 √2+1 √2 1
= −√ = −√ × = − √(√2 + 2)
2√2 2√2 √2 2




7𝜋 9𝜋 10𝜋
3. tan , tan , tan are in?
6 4 3

a) AP b) GP

c) HP d) None of these

A. The answer is b) GP
7𝜋 𝜋 𝜋 1
soln:- tan = tan (𝜋 + ) = tan =
6 6 6 √3

9𝜋 𝜋 𝜋
tan = tan (2𝜋 + ) = tan = 1
4 4 4

10𝜋 4𝜋 4𝜋 𝜋 𝜋
tan = tan (2𝜋 + ) = tan = tan (𝜋 + ) = tan ( ) = √3
3 3 3 3 3

1
Clearly , 1, √3 are in GP.
√3




𝑎𝑐𝑜𝑠𝜑+𝑏 𝜃
4. If 𝑐𝑜𝑠𝜃 = , then tan is equal to?
𝑎+𝑏𝑐𝑜𝑠𝜑 2

𝑎−𝑏 𝜑 𝑎+𝑏 𝜑
a) √ tan b) √ cos
𝑎+𝑏 2 𝑎−𝑏 2


𝑎−𝑏 𝜑
c) √ sin c) None of these
𝑎+𝑏 2


𝑎−𝑏 𝜑
A. The answer is a) √ tan
𝑎+𝑏 2

𝑎𝑐𝑜𝑠𝜑+𝑏
soln:- Now, 𝑐𝑜𝑠𝜃 =
𝑎+𝑏𝑐𝑜𝑠𝜑

Applying componendo and dividendo rule,
1−𝑐𝑜𝑠𝜃 [𝑎(1−𝑐𝑜𝑠𝜑)−𝑏(1−𝑐𝑜𝑠𝜑)]
=
1+𝑐𝑜𝑠𝜃 𝑎(1+𝑐𝑜𝑠𝜑)+𝑏(1+𝑐𝑜𝑠𝜑)