NCERT Solutions Class 11 Mathematics Chapter 3 Probability Download In Pdf

Chapter 3 Trigonometric Functions Download in pdf

**Question 1. **Find the radian measures corresponding to the following degree measures:

(i) 25Â°

(ii) â€“ 47Â°30

(iii)240Â°

(iv) 520Â°

**Question 2. **Find the degree measures corresponding to the following radian measurs
(Use
Ï€ 22
7
= ).

(i)
11
16

(ii) â€“ 4

(iii)
5Ï€
3

(iv)
7Ï€
6

**Question 3. ** A wheel makes 360 revolutions in one minute. Through how many radians does
it turn in one second?

**Question 4. **Find the degree measure of the angle subtended at the centre of a circle of
radius 100 cm by an arc of length 22 cm (Use
Ï€ 22
7
= ).

**Question 5. **In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of
minor arc of the chord.

**Question 6. **If in two circles, arcs of the same length subtend angles 60Â° and 75Â° at the
centre, find the ratio of their radii.

**Question 7. **Find the angle in radian through which a pendulum swings if its length is 75 cm
and th e tip describes an arc of length
(i) 10 cm (ii) 15 cm (iii) 21 cm

** Find the values of other five trigonometric functions in Exercises 1 to 5. **

**Question 1. **cos x = â€“
1
2 , x lies in third quadrant.

**Question 2. **sin x =
3
5, x lies in second quadrant.

**Question 3. ** cot x = 4
3
, x lies in third quadrant.

**Question 4. **sec x =
13
5 , x lies in fourth quadrant.

** Question 5. **tan x = â€“
5
12 , x lies in second quadrant.
Find the values of the trigonometric functions in Exercises 6 to 10.

**Question 6. **sin 765Â°

**Question 7. **cosec (â€“ 1410Â°)
8. tan
19Ï€
3
9. sin (â€“
11Ï€
3
)
10. cot (â€“
15Ï€
4
)

EXERCISE

**Prove that:**

**Question 1. **sin2
Ï€
6 + cos2 3
Ï€
â€“ tan2
â€“ 1
4 2
Ï€
=

**Question 2. **2sin2
6
Ï€
+ cosec2 7 cos2 3
6 3 2
Ï€ Ï€
=

**Question 3. ** cot2 cosec 5 3tan2 6
6 6 6
Ï€ Ï€ Ï€
+ + =

**Question 4. **2sin2 3 2cos2 2sec2 10
4 4 3
Ï€ Ï€ Ï€
+ + =

** Question 5. **Find the value of:

(i) sin 75Â°

(ii) tan 15Â°

**Find the principal and general solutions of the following equations: **

**
Question 6. **tan x = 3

**Question 7. **sec x = 2

**Question 8. ** cot x = âˆ’ 3

**Question 9. **cosec x = â€“ 2

Find the general solution for each of the following equations:

**Question 10. **cos 4 x = cos 2 x

**Question 11. **cos 3x + cos x â€“ cos 2x = 0

**Question 12. **sin 2x + cosx = 0 8. sec2 2x = 1â€“ tan 2x

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- Chapter 1 Sets
- chapter 2 Relations And Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations And Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences And Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction To Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability

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