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

Question 1.

cos x = – , x lies in third quadrant.

Solution :

According to question, cos x = and x lies in IIIrd quadrant

If x lies in IIIrd quadrant 180° ≤ x ≤ 270°, (π ≤ x ≤ π)

Hence, in it tan and cot are only in positive and other trigonometric functions are in negative.

Question 2.

cot x = , 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 = , 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)

=

Hence, sin 765° =

Question 5.

Find the value of tan

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 = = √3

Question 6.

Find the value of sin

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

Solution:

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

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