NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.2
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1. Find the value of other five trigonometric function when cos x = -1/2, x lies in third quadrant.
Answer
Since x lies in the 3rd quadrant
Cos x = -1/2
∴ Sin x = - √(1 – cos2x) (∵ x lies in III rd quadrant)
=- √(1 – ¼) = -√3/2
Tan x = √3
Cot x = 1/√3
Sec x = (1/cos x) = -2
Cosec x = 1/sin x = - 2/√3
2. Find the value of other five trigonometric function when sin x=3/ 5, x lies in second quadrant.
Answer
Since x lies in the second quadrant
sin x = 3/5 given
cos x = - √(1 – sin2 x) (∵ x lies in II quadrant)
= - √(1 – 9/25) = -4/5
Sec x = -5/4, tan x = - ¾
Cosec x = 5/3, cot x = - 4/3
3. cot x = 3/4, x lies in third quadrant.
Answer
∴ cot x = 3/4 = -3/-4
Let MP = -4, OM = -3, then
OP = √(MP2 + OM2) = √(16 + 9)
= √25 = 5
Now sin x = MP/OP = -4/5
cot x = OM/MP = 3/4
cos x = OM/OP = -3/5
sec x = OP/OM = 5/-3 = -5/3
tan x = 4/3 [Given]
cosec x = OP/MP = 5/-4 = -5/4
4. sec x = 13/5, x lies in fourth quadrant.
Answer
Since x lies in fourth quadrant.
4. sec x = 13/5, x lies in fourth quadrant.
Answer
Since x lies in fourth quadrant.
∴ sec x = 13/5 => OP/OM = 13/5
Let OP = 13, OM = 5. Then,
MP = -√(OP2 - OM2)
= - √(169 - 25)
- √144 = -12
Now, sin x = MP/OP = -12/13
cot x = OM/MP = 5/12 = -5/12
cos x = OM/OP = 5/3
sec x = OP/OM = 13/5
tan x = MP/OM = -12/5
cosec x = OP/MP = 13/-12 = -13/12
5. Find the value of other five trigonometric function when tan x = - 5/12, x lies in second quadrant.
Answer
x lies in the second quadrant
5. Find the value of other five trigonometric function when tan x = - 5/12, x lies in second quadrant.
Answer
x lies in the second quadrant
tan x = -5/12
cot x = - 12/5
sec x = - √(1 + tan2x) ( ∵ x lies in II quadrant)
= - √(1 + 25/144) = -13/12
cos x = -12/13
sin x = √1- cos2x = 5/13
cosec x = 13/5
6. Find the values of the following trigonometric sin 765°.
Answer
sin 765° = sin (8 × 90° + 45°)
= sin 45° 1/√2
7. Find the values of the following trigonometric cosec (– 1410°).
Answer
cosec (–1410°)
= cosex(-1410 + 1440) = cosec(30) = 2
8. Find the values of the following trigonometric tan 19Ï€/3.
Answer
tan 19Ï€/3 = tan (6 Ï€ + Ï€/3) = tan Ï€/3 = √3
9. Find the values of the following trigonometric 11 sin (-11 π/3)
Answer
sin (-11π/3) = -sin 11π/3 [ sin (-θ) = -sinθ]
= -sin(4Ï€ – Ï€/3) = - (-sin Ï€/3)
= sin Ï€/3 = √3/2
10. Find the values of the following trigonometric cot(- 15Ï€/4)
Answer
cot(- 15π/4) = - cot 15π/4 [ cot(-θ) = -cotθ]
= -cot(4Ï€ – Ï€/4) = -cot(- Ï€/4)
=-(-cot π/4) = cot. π/4 = 1
6. Find the values of the following trigonometric sin 765°.
Answer
sin 765° = sin (8 × 90° + 45°)
= sin 45° 1/√2
7. Find the values of the following trigonometric cosec (– 1410°).
Answer
cosec (–1410°)
= cosex(-1410 + 1440) = cosec(30) = 2
8. Find the values of the following trigonometric tan 19Ï€/3.
Answer
tan 19Ï€/3 = tan (6 Ï€ + Ï€/3) = tan Ï€/3 = √3
9. Find the values of the following trigonometric 11 sin (-11 π/3)
Answer
sin (-11π/3) = -sin 11π/3 [ sin (-θ) = -sinθ]
= -sin(4Ï€ – Ï€/3) = - (-sin Ï€/3)
= sin Ï€/3 = √3/2
10. Find the values of the following trigonometric cot(- 15Ï€/4)
Answer
cot(- 15π/4) = - cot 15π/4 [ cot(-θ) = -cotθ]
= -cot(4Ï€ – Ï€/4) = -cot(- Ï€/4)
=-(-cot π/4) = cot. π/4 = 1