Exercise 4.5 - Chapter 4 - Trigonometry - 11th Business Maths Guide Samacheer Kalvi Solutions

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Exercise 4.5

 Text Book Back Questions and Answers

Question 1.
The degree measure of π8 is:
(a) 20°60′
(b) 22°30′
(c) 22°60′
(d) 20°30′
Answer:
(b) 22°30′
Hint:
We know that, one radian 

Question 2.
The radian measure of 37°30′ is:

Answer:

Hint:

Question 3.
If tan θ =  and θ lies in the first quadrant then cos θ is:

Answer:

Hint:

Question 4.
The value of sin 15° is:

 

Answer:

Question 5.
The value of sin(-420°)

Answer:

Hint:

sin(-420°) = -sin(420°) [∵ sin(-θ) = -sin θ]
= -sin(360° + 60°)
= -sin 60°

Question 6.
The value of cos(-480°) is:

Answer:

Hint:
cos(-480°) = cos 480° [∵ cos(-θ) = cos θ]
= cos(360° + 120°)
= cos 120°
= cos(180° – 60°)
= -cos 60°

Question 7.
The value of sin 28° cos 17° + cos 28° sin 17°

Answer:

Hint:
sin 28° cos 17° + cos 28° sin 17° = sin(28° + 17°)
This is of the form sin(A + B), A = 28°, B = 17°
= sin 45°

Question 8.
The value of sin 15° cos 15° is:
(a) 1

Answer:

Question 9.
The value of sec A sin(270° + A) is:
(a) -1
(b) cos² A
(c) sec² A
(d) 1
Answer:
(a) -1
Hint:

Question 10.
If sin A + cos A = 1 then sin 2A is equal to:
(a) 1
(b) 2
(c) 0
(d) 1/2
Answer:
(c) 0
Hint:
Given sin A + cos A = 1
Squaring both sides we get
sin² A + cos² A + 2 sin A cos A = 1
1 + sin 2A = 1
sin 2A = 0

Question 11.
The value of cos² 45° – sin² 45° is:

Answer:

(c) 0
Hint:
cos² 45° – sin² 45°
= cos 2 × 45° (∵ cos² A – sin² A = cos 2A)
= cos 90°
= 0

Question 12.
The value of 1 – 2 sin² 45° is:
(a) 1

Answer:
(d) 0
Hint:
1 – 2 sin² 45°
= cos(2 × 45°) [∵ cos 2A = 1 – 2 sin² A]
= cos 90°
= 0

Question 13.
The value of 4 cos³ 40° – 3 cos 40° is

Answer:

(b) −1/2
Hint:

4 cos³ 40° – 3 cos 40°
= cos (3 × 40°) [∵ cos 3A = 4 cos³ A – 3 cos A]
= cos 120°
= cos (180° – 60°)
= -cos 60°

Question 14.
The value of 

Question 15.
If sin A =  then 4 cos³ A – 3 cos A is:
(a) 1
(b) 0

sin A = sin 30°
∴ A = 30°
[∵ 4 cos³ A – 3 cos A = cos 3A]
= cos(3 × 30°)
= cos 90°
= 0

Question 16.
The value of

Question 17.
The value of cosec^-1

Question 18.

Answer:

Question 19.
If α and β be between 0

Question 20.

(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(c) 3
Hint:
Given tan

Question 21.

(c) 1 – tan x
(d) 1 + tan x
Answer:

Question 22.

Question 23.
The value of

Question 24.
If p sec 50° = tan 50° then p is:
(a) cos 50°
(b) sin 50°
(c) tan 50°
(d) sec 50°
Answer:
(b) sin 50°
Hint:
p sec 50° = tan 50°

Question 25.

(a) cos² x – sin² x
(b) sin² x – cos² x
(c) 1
(d) 0
Answer:
(d) 0
Hint:

= cos x × sin x – cos x × sin x
= 0