Rajasthan Board RBSE Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2

Question 1.
cos x = – $\frac { 1 }{ 2 }$ , x lies in third quadrant.
Solution :
According to question, cos x = $\frac { 1 }{ 2 }$ and x lies in IIIrd quadrant

If x lies in IIIrd quadrant 180° ≤ x ≤ 270°, (π ≤ x ≤ $\frac { 3 }{ 2 }$ π)
Hence, in it tan and cot are only in positive and other trigonometric functions are in negative.

Question 2.
cot x = $\frac { 3 }{ 4 }$ , x lies in third quadrant.
Solution:

According to rule ASTC all the trigonometric functions are in negative in IIIrd quadrant except tan and cot.

Question 3.
sec x = $\frac { 13 }{ 5 }$ , x lies in fourth quadrant.
Solution:

Question 4.
Find the value of sin 765°
Solution :
we know that values of sin x repeats after an interval of 2π
So, sin (765°) = sin (720° + 45°)
= sin (2 x 360° + 45°)
= sin 45°
(∵ After repetition it wil comes in 1st quardrant)
= $\frac { 1 }{ \sqrt { 2 } }$
Hence, sin 765° = $\frac { 1 }{ \sqrt { 2 } }$

Question 5.
Find the value of tan $\frac { 19\pi }{ 3 }$
Solution:
We know that values of tan x repeats after an interval of Ilnd quardrant so,

(After repetition it will comes in 1st quardrant and all trigonometric ratios are positive in 1st quadrant.)
= √3
Hence, tan = $\left( -\frac { 19\pi }{ 3 } \right)$ = √3

Question 6.
Find the value of sin $\left( -\frac { 11\pi }{ 3 } \right)$
Solution:
We know that values of sin x repeats after an interval of 2π.

(So, this angle will be in IV quadrant in which sin is negative.)