RBSE Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2

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

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

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

Question 2.
cot x = [latex]\frac { 3 }{ 4 } [/latex], 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 = [latex]\frac { 13 }{ 5 } [/latex], 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)
= [latex]\frac { 1 }{ \sqrt { 2 } } [/latex]
Hence, sin 765° = [latex]\frac { 1 }{ \sqrt { 2 } } [/latex]

Question 5.
Find the value of tan [latex]\frac { 19\pi }{ 3 } [/latex]
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 = [latex]\left( -\frac { 19\pi }{ 3 } \right) [/latex] = √3

Question 6.
Find the value of sin [latex]\left( -\frac { 11\pi }{ 3 } \right) [/latex]
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.)

Question 7.
Find the value of cot [latex]\left( -\frac { 15\pi }{ 4 } \right) [/latex]
Solution:

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

RBSE Solutions for Class 11 Maths