NCERT Solutions
Class 11 - Mathematics - Chapter 3: TRIGONOMETRIC FUNCTIONS
EXERCISE 3.2

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Question. 1

cos x = -\( \dfrac{1}{2} \), x lies in the third quadrant. Find the other five trigonometric ratios.

Answer:

\( \sin x = -\dfrac{\sqrt{3}}{2} \), \( \csc x = -\dfrac{2}{\sqrt{3}} \), \( \sec x = -2 \), \( \tan x = \sqrt{3} \), \( \cot x = \dfrac{1}{\sqrt{3}} \)

Question. 2

sin x = \( \dfrac{3}{5} \), x lies in second quadrant. Find the other five trigonometric ratios.

Answer:

\( \csc x = \dfrac{5}{3} \), \( \cos x = -\dfrac{4}{5} \), \( \sec x = -\dfrac{5}{4} \), \( \tan x = -\dfrac{3}{4} \), \( \cot x = -\dfrac{4}{3} \)

Question. 3

cot x = \( \dfrac{3}{4} \), x lies in third quadrant. Find the other five trigonometric ratios.

Answer:

\( \sin x = -\dfrac{4}{5} \), \( \csc x = -\dfrac{5}{4} \), \( \cos x = -\dfrac{3}{5} \), \( \sec x = -\dfrac{5}{3} \), \( \tan x = \dfrac{4}{3} \)

Question. 4

sec x = \( \dfrac{13}{5} \), x lies in fourth quadrant. Find the other five trigonometric ratios.

Answer:

\( \sin x = -\dfrac{12}{13} \), \( \csc x = -\dfrac{13}{12} \), \( \cos x = \dfrac{5}{13} \), \( \tan x = -\dfrac{12}{5} \), \( \cot x = -\dfrac{5}{12} \)

Question. 5

tan x = -\( \dfrac{5}{12} \), x lies in second quadrant. Find the other five trigonometric ratios.

Answer:

\( \sin x = \dfrac{5}{13} \), \( \csc x = \dfrac{13}{5} \), \( \cos x = -\dfrac{12}{13} \), \( \sec x = -\dfrac{13}{12} \), \( \cot x = -\dfrac{12}{5} \)

Question. 6

Find \( \sin 765^\circ \).

Answer:

\( \dfrac{1}{\sqrt{2}} \)

Question. 7

Find \( \csc(-1410^\circ) \).

Answer:

2

Question. 8

Find \( \tan \left( \dfrac{19\pi}{3} \right) \).

Answer:

\( \sqrt{3} \)

Question. 9

Find \( \sin\left( -\dfrac{11\pi}{3} \right) \).

Answer:

\( \dfrac{\sqrt{3}}{2} \)

Question. 10

Find \( \cot\left( -\dfrac{15\pi}{4} \right) \).

Answer:

1