## 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)

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