Important Questions Class 11 Maths Chapter 3
Important Questions Class 11 Mathematics Chapter 3
Important Questions for CBSE Class 11 Mathematics Chapter 3 – Trigonometric Functions
Trigonometric functions Class 11 Important Questions have been prepared for Class 11 students to help them score higher in the exams. The important Questions for Trigonometric Functions are prepared by subject matter experts in accordance with the latest CBSE guidelines.
The Class 11 Mathematics Trigonometric Functions Important Questions include step-by-step solutions for questions ranging from simple to difficult. Furthermore, students can easily access these study materials from Extramarks to have a ready reference to the chapters and questions whenever they need it. Students can also make notes and mark them for quick revision based on the important questions. They can easily develop command over trigonometric functions as they answer these important questions.
CBSE Class 11 Mathematics Chapter-3 Important Questions
Study Important Questions for Class 11 Mathematics Chapter 3 – Trigonometric Functions
Students can view the set of important questions given below.
Q1. Prove that sin5x−2sin3x+sinx / cos5x−cosx =tanx
A1. Starting with the left-hand side and using the trigonometric difference identities for the sine function, we obtain
L.H.S.=sin5x+sinx−2sin3x / cos5x−cosx
=2sin3x.cos2x−2sin3x / −2sin3x.sin2x
=2sin3x(cos2x−1)/ −2sin3x.sin2x
=−(1−cos2x)/−sin2x
=2sin2x / 2sinx.cosx
=sinx / cosx
=tanx
=R.H.S.
Q2. Prove that cos6x=32cos2x − 48cos4x + 18cos2x − 1
A2. Starting with the left-hand side and using the trigonometric identities for the cosine function, we obtain
L.H.S.
=cos6x
=cos2(3x)=2Cos23x−1
=cos2(3x)
=2(4cos3x−3cosx)2−1
=2[16cos6x+9cos2x−24cos4x]−1
=32cos6x+18cos2x−48cos4x−1
=32cos6x−48cos4x+18cos2x1
=R.H.S.
Q3. Prove that sin(x+y)/sin(x−y)=tanx+tany/tanx−tany
A3. Starting with the left-hand side and using the trigonometric difference formula for the sine function, we get
L.H.S.
=sin(x+y)/sin(x−y)
=sinx.cosy+cosx.siny/sinx.cosy−cosx.siny
Dividing numerator and denominator by cosx.cosy
=tanx+tany/tanx−tany
=R.H.S.
Q4. The minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes?
A4. Analysing the given information, we have,
r=1.5cm
Angle made in 60min=360∘
Angle made in 1min=6∘
Angle made in 40min=6∘×40∘=240∘
Calculating the arc distance
θ=l/r
240×π/180=l/1.5
2×3.14=l
6.28=l
l=6.28cm
Q6. Show that tan 3x. tan 2x. tan x = tan 3x tan 2x tan x
A6. Let us start with tan3x and we know 3x=2x+x
tan3x=tan(2x+x)
tan3x/1=tan2x+tanx/1−tan2x.tanx
tan3x(1−tan2x.tanx)=tan2x+tanx
tan3x−tan3x.tan2x.tanx=tan2x+tanx
tan3x.tan2x.tanx=tan3x−tan2x−tanx
Q7. A wheel makes 360 revolutions in 1 minute. How many radians does it turn in 1 second?
A7.
Given,
Number of revolutions made in 60s=360
Number of revolutions made in 1s=360/60
Angle moved in 6 revolutions = 2π × 6 = 12π
CBSE Class 11 Mathematics Chapter-3 Important Questions
Given below is the complete set of Important Questions for Trigonometric Functions, which can be accessed by clicking the link provided.
Class 11 Mathematics Chapter 3 Important Questions- What are Trigonometric Functions?
In layman’s terms, trigonometric functions are functions of triangle angles. On the basis of these functions, it defines the relationship between the sides and angles of a triangle. The sine, cosine, secant, cosecant, tangent, and cotangent are trigonometric functions. It is also referred to as circular functions. Several trigonometric formulas and identities can be used to define the relationship between angles and functions.
Tips to Score Marks in Trigonometric Functions
One of the most important chapters in Class 11 Mathematics is the Trigonometric Function. Trigonometry was developed primarily to solve geometric problems involving triangles. Students can easily score high marks in the examinations by practising the important questions of Mathematics Class 11 Trigonometric Functions. When students prepare for these important questions, they can also learn several tricks and shortcuts to answer the questions quickly. Furthermore, students must concentrate on the trigonometric function formulas that are required to solve the sums. Students should not skip this chapter because it covers many important topics, such as designing electronic circuits, calculating tide heights, and so on.
Discuss the Trigonometric Tables and formulas
The Formula for Function of Trigonometric Ratios
| Formulas for Angle θ | Reciprocal Identities |
| sin θ = Opposite Side/ Hypotenuse | sin θ = 1/cosec θ |
| cos θ = Adjacent Side/ Hypotenuse | cos θ = 1/sec θ |
| sec θ = Hypotenuse/ Adjacent Side | sec θ = 1/cos θ |
| cosec θ = Hypotenuse/ Opposite | cosec θ = 1/sin θ |
| tan θ = Opposite Side/ Hypotenuse | tan θ = 1/cot θ |
| cot θ = Adjacent Side/ Opposite | cot θ = 1/tan θ |
Trigonometric Table
| Trigonometric Ratios/Angle = θ in degree | 0° | 30° | 45° | 60° | 90° |
| Sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| Cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| Sec θ | 1 | 2/√3 | √2 | 2 | ∞ |
| Cosec θ | ∞ | 2 | √2 | 2/√3 | 1 |
| Tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
| Cot θ | ∞ | √3 | 1 | 1/√3 | 0 |
Important Questions for Class 11 Mathematics Chapter 3 Based on Exercise
- In one minute, an engine makes 360 revolutions. How many radians will it turn in a second?
Answer:
Provided,
An engine’s total number of revolutions per minute = 360
1 minute equals 60 seconds
As a result, the number of revolutions in one second = 360 / 60 = 6.
360° is the angle formed in one revolution.
Angles are formed in six revolutions, which equals six 360°.
The angle in radians measured over six revolutions = 6 360 / 180
= 6 × 2 × π
= 12π
As a result, the engine rotates 12 radians in one second.
Importance of Downloading Class 11 Mathematics Chapter 3 Important Questions
Students will gain a thorough understanding of Trigonometric Functions by accessing the Important Questions for Class 11 Mathematics Chapter 3. Here are some advantages:
- They can make important notes for the exam.
- They will have access to all Trigonometric Functions Class 11 Important Questions.
- They can use it as a ready reference resource.
It will help them understand theexamination’s question pattern.
Q.1
If A + B = 225°, then tan A + tan B + tan A × tan B is equal to:
1
0
1
3
Marks:1
Ans
tan (A + B) = tan (225) = tan (180+45) = tan 45 = 1
Now, tan(A+B) = (tan A+tan B)/(1 tan A × tan B)
(tan A + tan B)/(1? tan A × tan B) = 1
tan A + tan B + tan A × tan B = 1
Q.2
if ? is an acute angle and sin (?/2) = x-12xthen tan ? is
Marks:1
Ans
tan?=sin?cos?= 2sin?(?/2)?cos?(?/2)1?sin2(?/2)
tan?=2x?12x?1?x?12×1?2x?12x = x2?1
Q.3
Which is greater ? sin1or sin1? Justify your answer.
Marks:4
Ans
First, we shall convert 1 into degree µ =180°
1=180 =180227 =180—722 =90—711 =63011 1=57.27
sin1=sin 57.27bHence, sin1 is greater than sin1.
Q.4
If three angles A, B, C, are in A.P. Prove that: cotB=sinA-sinCcosC-cosA
Marks:3
Ans
R.H.S=sinA-sinCcosC-cosA
=2sinA-C2cosA+C22sinA+C2sinA-C2
=cotA+C2=cotB=L.H.S µA,B,C are in A.P 2B=A+C
Q.5
Show that: 2+2+2+2cos8?=2cos?
Marks:4
Ans
LH.S=2+2+2(1+cos 8¸) =22+2—2cos2 4 µ 1+cos 8 =2cos2 4 =2+2+4cos2 4 =2+2+2cos 4
=2+21+cos4 =2+2-2cos22µ1+cos4 =2cos22=2+4cos22 =2+2cos2 =21+cos2 =2.2cos2 =2cos=R ·H.S
FAQs (Frequently Asked Questions)
1. What are the fundamental trigonometric functions?
Trigonometric functions are fundamental functions in mathematics that are used to denote the relationship between the angles of a right-angled triangle and the lengths of its sides.
There are six trigonometric ratios in total, with sine, cosine, and tangent serving as the fundamental three. The other three are called cosecant, secant, and cotangent and are described in relation to previously discussed basic functions.
In a given right-angled triangle, the following values of these ratios are calculated for a specific angle θ in terms of its sides:
sin θ = opposite side / hypotenuse
cos θ = adjacent side / hypotenuse
tan θ = sin θ / cos θ = opposite site / adjacent side
cosec θ = 1 / sin θ
sec θ = 1 / cos θ
cot θ = cos θ / sin θ = 1 / tan θ
2. What is the relationship between Radians and Degrees?
A radian (abbreviated rad or c) is a standard unit of measurement for angles based on the relationship between the length of an arc and the radius of a circle.
rad = arc length / circle radius
Many times, you will be required to convert given angle values from radians to degrees.The relationship between these two units can be deduced as follows.
The circumference C of a full circle with radius r and angle 360o is equal to the arc length.
Therefore, arc length = C = 2πr.
From the first relation, 360o in radians will be
rad = 2πr / r = 2π
Therefore, 2π rad = 360o,
that is, 1 rad = 180o / π.
This brings us to the final relationship, that is, degree = radian x 180 / π.
3. What are the practical applications of trigonometry?
Trigonometry has a wide range of applications in marine biology, navigation, aviation, and other fields because it involves the relationship between sides and angles, finding the height, and calculating the distance. It is also used to solve complex mathematical problems, such as those incalculus and algebra.
4. What are the angles of trigonometry?
You will come across several new terms that are used in trigonometry questions as you study Chapter 3 Trigonometry of Class 11 Mathematics. The angles of trigonometry are the most important of these. These are essentially functions that aid in the relationship of triangle sides and angles. The sine, cosine, and tangent are abbreviated as sin, cos, and tan. Secant, cosecant, and cotangent are the inverse functions or angles, abbreviated as sec, cosec, and cot.
5. Name the Six Trigonometric Functions.
The six trigonometric functions are sine, cosine, tan, cosec, sec, and cot.
