## NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Exercise 3.2

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1.Â 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 quadrantÂ

Cos x = -1/2

âˆ´ Sin x = - âˆš(1 â€“ cos2x) (âˆµ x lies in III rdÂ quadrant)Â

=- âˆš(1 â€“ Â¼) = -âˆš3/2

Tan x = âˆš3

Cot x = 1/âˆš3

Sec x = (1/cos x) = -2

Cosec x = 1/sin x = - 2/âˆš3

2.Â Find the value of other five trigonometric function whenÂ sin x=3/ 5, x lies in second quadrant.Â

**Answer**

Since x lies in the second quadrant

sin x = 3/5 given

cos x = - âˆš(1 â€“ sin2 x) (âˆµ x lies in II quadrant)

= - âˆš(1 â€“ 9/25) = -4/5

Sec x = -5/4, tan x = - Â¾

Cosec x = 5/3, cot x = - 4/3

3.Â cot x = 3/4, x lies in third quadrant.

**Answer**

âˆ´Â cot x = 3/4 = -3/-4

Let MP = -4, OM = -3, then

OP =Â âˆš(MP

^{2}Â + OM^{2}) =Â âˆš(16 + 9)
=Â âˆš25 = 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.Â sec x = 13/5, x lies in fourth quadrant.

Since x lies in fourth quadrant.

4.Â sec x = 13/5, x lies in fourth quadrant.

**Answer**Since x lies in fourth quadrant.

âˆ´Â sec x = 13/5 => OP/OM = 13/5

Let OP = 13, OM = 5. Then,

MP = -âˆš(OP

^{2}Â - OM^{2})
= -Â âˆš(169 - 25)

-Â âˆš144 = -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.

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 = -Â âˆš(1 + tan

^{2}x) (Â âˆµÂ x lies in II quadrant)
= -Â âˆš(1 + 25/144) = -13/12

cos x = -12/13

sin x =Â Â âˆš

*1- cos*^{2}*x*Â = 5/13
cosec x = 13/5

6. Find the values of the following trigonometric sin 765Â°.

sin 765Â° = sin (8 Ã— 90Â° + 45Â°)

= sin 45Â° 1/âˆš2

7.Â Find the values of the following trigonometric cosec (â€“ 1410Â°).

cosec (â€“1410Â°)

= cosex(-1410 + 1440) = cosec(30) = 2

8.Â Find the values of the following trigonometric tan 19Ï€/3.

tan 19Ï€/3 = tan (6 Ï€ + Ï€/3) = tan Ï€/3 = âˆš3

9.Â Find the values of the following trigonometric 11 sin (-11 Ï€/3)

sin (-11Ï€/3) = -sin 11Ï€/3 [ sin (-Î¸) = -sinÎ¸]

= -sin(4Ï€ â€“ Ï€/3) = - (-sin Ï€/3)

= sin Ï€/3 = âˆš3/2

10.Â Find the values of the following trigonometric cot(- 15Ï€/4)

cot(- 15Ï€/4) = - cot 15Ï€/4 [ cot(-Î¸) = -cotÎ¸]

= -cot(4Ï€ â€“ Ï€/4) = -cot(- Ï€/4)

=-(-cot Ï€/4) = cot. Ï€/4 = 1

6. Find the values of the following trigonometric sin 765Â°.

**Answer**sin 765Â° = sin (8 Ã— 90Â° + 45Â°)

= sin 45Â° 1/âˆš2

7.Â Find the values of the following trigonometric cosec (â€“ 1410Â°).

**Answer**cosec (â€“1410Â°)

= cosex(-1410 + 1440) = cosec(30) = 2

8.Â Find the values of the following trigonometric tan 19Ï€/3.

**Answer**tan 19Ï€/3 = tan (6 Ï€ + Ï€/3) = tan Ï€/3 = âˆš3

9.Â Find the values of the following trigonometric 11 sin (-11 Ï€/3)

**Answer**sin (-11Ï€/3) = -sin 11Ï€/3 [ sin (-Î¸) = -sinÎ¸]

= -sin(4Ï€ â€“ Ï€/3) = - (-sin Ï€/3)

= sin Ï€/3 = âˆš3/2

10.Â Find the values of the following trigonometric cot(- 15Ï€/4)

**Answer**cot(- 15Ï€/4) = - cot 15Ï€/4 [ cot(-Î¸) = -cotÎ¸]

= -cot(4Ï€ â€“ Ï€/4) = -cot(- Ï€/4)

=-(-cot Ï€/4) = cot. Ï€/4 = 1