NCERT Solutions for Class 11 Maths Chapter 3 Ex 3.2

Get Free NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 PDF in Hindi and English Medium. Trigonometric Functions Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Trigonometric Functions Exercise 3.2 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 3 Class 11 Trigonometric Functions Ex 3.2 provided in NCERT Textbook.

• Trigonometric Functions Class 11 Ex 3.1
• Trigonometric Functions Class 11 Ex 3.2
• Trigonometric Functions Class 11 Ex 3.3
• Trigonometric Functions Class 11 Ex 3.4
• Trigonometric Functions Class 11 Miscellaneous Exercise
• त्रिकोणमितीय फलन प्रश्नावली 3.1 का हल हिंदी में
• त्रिकोणमितीय फलन प्रश्नावली 3.2 का हल हिंदी में
• त्रिकोणमितीय फलन प्रश्नावली 3.3 का हल हिंदी में
• त्रिकोणमितीय फलन प्रश्नावली 3.4 का हल हिंदी में
• त्रिकोणमितीय फलन विविध प्रश्नावली का हल हिंदी में
• Trigonometry Formulas
• Trigonometry Functions Class 11 Notes
• NCERT Exemplar Class 11 Maths Chapter 3 Trigonometric Functions
• Trig Cheat Sheet
• JEE Main Trigonometry Previous Year Questions

Free download NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCE1RT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 3 Ex 3.2

Ex 3.2 Class 11 Question 1:

Find the values of other five trigonometric functions if cos x = – \(\frac{1}{2}\) x lies in third quadrant.

Ans:

Ex 3.2 Class 11  Question 2:

Find the values of other five trigonometric functions if sin x = \(\frac{3}{5}\), x lies in second quadrant.

Ans:

sin x = \(\frac{3}{5}\)

cosec x = \(\frac{1}{\sin x}=\frac{1}{\left(\frac{3}{5}\right)}=\frac{5}{3}\)
sin ² x + cos ² x = 1
⇒ cos ² x = 1 – sin ² x
⇒ cos ² x = 1 – (\(\frac{3}{5}\)) ²

⇒ cos ² x = 1 – \(\frac{9}{25}\)

⇒ cos ² x = \(\frac{16}{25}\)

⇒ cos x = ± \(\frac{4}{5}\)
Since x lies in the 2nd quadrant, the value of cos x will be negative

Ex 3.2 Class 11  Question 3:

Find the values of other five trigonometric functions if cot x = \(\frac{3}{4}\), x lies in third quadrant.

Ans:

⇒ \(\frac{4}{3}=\frac{\sin x}{\frac{-3}{5}}\)

⇒ sin x = \(\left(\frac{4}{3}\right) \times\left(\frac{-3}{5}\right)=-\frac{4}{5}\)

⇒ cosec x = \(\frac{1}{\sin x}=-\frac{5}{4}\).

Ex 3.2 Class 11 Question 4:

Find the values of other five trigonometric functions if sec x = \(\frac{13}{5}\), x lies in fourth quadrant.

Ans:

Ex 3.2 Class 11 Question 5:

Find the values of other five trigonometric functions if tan x = \(\frac{5}{12}\), x lies in second quadrant.

Ans:

an x = – \(\frac{5}{12}\)

cot x = \(\frac{1}{\tan x}=\frac{1}{\left(-\frac{5}{12}\right)}=-\frac{12}{5}\)

1 + tan ² x = sec ² x

Ex 3.2 Class 11 Question 6:

Find the value of the trigonometric function sin 765°.

Ans:
It is known that the values of sin x repeat after an interval of 2π or 360°.
∴ sin 765° = sin (2 × 360° + 45°)
= sin 45° = 1
Ex 3.2 Class 11 Question 7:

Find the value of the trigonometric function cosec (- 1410°).

Ans:
It is known that the values of cosec x repeat after an interval of 2π or 360°.
∴ cosec (- 1410°) = cosec (- 1410° + 4 x 360°)
= cosec (- 1410° + 1440°)
= cosec 30° = 2.
Ex 3.2 Class 11 Question 8:

Find the value of the trigonometric function tan \(\frac{19 \pi}{3}\).

Ans:

It is known that the values of tan x repeat after an interval of π or 180°.
∴ \(\tan \frac{19 \pi}{3}=\tan 6 \frac{1}{3} \pi\)

= \(\tan \left(6 \pi+\frac{\pi}{3}\right)=\tan \frac{\pi}{3}\)

= tan 60° = √3.

Ex 3.2 Class 11 Question 9:

Find the value of the trigonometric function sin \(\left(-\frac{11 \pi}{3}\right)\).

Ans:

It is known that the values of cot x repeat after an interval of π or 180°.

∴ \(\sin \left(\frac{11 \pi}{3}\right)=\sin \left(-\frac{11 \pi}{3}+2 \times 2 \pi\right)\)

= \(\sin \left(\frac{\pi}{3}\right)=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\)

Ex 3.2 Class 11 Question 10:

Find the value of the trigonometric function cot \(\left(-\frac{15 \pi}{4}\right)\).

Ans:

It is known that the values of cot x repeat after an interval of ir or 1800.
∴ \(\cot \left(-\frac{15 \pi}{4}\right)=\cot \left(-\frac{15 \pi}{4}+4 \pi\right)=\cot \frac{\pi}{4}\) = 1.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions in Hindi Medium

निम्नलिखित प्रश्नों में से पाँच अन्य त्रिकोणमितीय फलनों का मान ज्ञात कीजिए।

प्रश्न 1.
cos x = \(\frac { -1 }{ 2 }\) , x तीसरे चतुर्थाश में स्थित है।

प्रश्न 2.
sin x = \(\frac { 3 }{ 5 }\) , x दूसरे चतुर्थाश में स्थित है।

प्रश्न 3.
cot x = \(\frac { 3 }{ 4 }\) , x तृतीय चतुर्थाश में स्थित है।
हलः
cot x = \(\frac { 3 }{ 4 }\)
OA = 3 इकाई

प्रश्न 4.
sec x = \(\frac { 13 }{ 5 }\) , x चतुर्थ चतुर्थाश में स्थित है।

प्रश्न 5.
tan x = \(\frac { -5 }{ 12 }\) , x दुसरे चतुर्थाश में स्थित है।

प्रश्न संख्या 6 से 10 तक के मान ज्ञात कीजिए:
प्रश्न 6.
sin 765°

प्रश्न 7.
cosec (-1410)°

प्रश्न 8.
tan \(\frac { 19\pi }{ 3 }\)

प्रश्न 9.
sin (\(\frac { -11\pi }{ 3 }\)).

प्रश्न 10.
cot (\(\frac { -15\pi }{ 4 }\)).