## 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)

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