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.)
Question 7.
Find the value of cot \(\left( -\frac { 15\pi }{ 4 } \right) \)
Solution:
(So, this angle will be in IV quadrant. In which cot is negative)
