Trigonometry Study Materials PDF: The most important task of trigonometry is to find the remaining side and angle of a triangle when some of its side and angles are given. This problem is solved by using some ratio of sides of a triangle with respect to its acute angle.
This ratio of acute angle are called the trigonometric ratio of angle. Let us now define various trigonometric ratio.
Trigonometry Study Materials PDF For Competitive Exams
Article Name | Trigonometry Study Materials PDF With Practice Questions Worksheet |
Category | Study Materials |
Name Of The Lesson | Trigonometry |
Name Of The Subject | Mathematics |
Important For | Competitive Exams & Other Exams |
Post Included | Important Formulae, Notes, Study Materials, Practice Questions Worksheets PDF |
Quality | Best |
Format | |
Official Website | https://www.educationlearnacademy.com/ |
Trigonometry Basics
The concept of Trigonometry is given by a Greek mathematician Hipparchus. Trigonometry is all about a right-angled triangle.
It is one of those divisions in mathematics that helps in finding the angles and missing sides of a triangle by the help of trigonometric ratios.
The angles are either measured in radians or degrees. The usual trigonometry angles are 0°, 30°, 45°, 60° and 90°, which are commonly used.
Six Important Trigonometric Functions
The six important trigonometric functions (trigonometric ratios) are calculated by the below formulas using above figure. It is necessary to get knowledge regarding the sides of the right-angle triangle because it defines the set of important trigonometric functions.
Functions | Abbreviation | Relationship to sides of a right triangle |
Sine Function | sin | Opposite side/ Hypotenuse |
Tangent Function | tan | Opposite side / Adjacent side |
Cosine Function | cos | Adjacent side / Hypotenuse |
Cosecant Function | cosec | Hypotenuse / Opposite side |
Secant Function | sec | Hypotenuse / Adjacent side |
Cotangent Function | cot | Adjacent side / Opposite side |
Trigonometry Ratios Table
The standard angles of trigonometrical ratios are 0°, 30°, 45°, 60° and 90°. The values of trigonometrical ratios of standard angles are very important to solve trigonometrical problems.
The values of trigonometrical ratios of standard angles are very important to solve the trigonometrical problems. Therefore, it is necessary to remember the value of the trigonometrical ratios of these standard angles. The sine, cosine and tangent of the standard angles are given below in the table.
Trigonometry Formula
The Trigonometric formulas or Identities are the equations which are true in the case of Right-Angled Triangles. Some of the special trigonometric identities are as given below –
1. Pythagorean Identities
- sin ² θ + cos ² θ = 1
- tan 2 θ + 1 = sec2 θ
- cot2 θ + 1 = cosec2 θ
- sin 2θ = 2 sin θ cos θ
- cos 2θ = cos² θ – sin² θ
- tan 2θ = 2 tan θ / (1 – tan² θ)
- cot 2θ = (cot² θ – 1) / 2 cot θ
2. Sum and Difference identities-
For angles A and B, we have the following relationships:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) – sin(A)sin(B)
- tan(A + B) = tan(A) + tan(B)/1−tan(A) tan(B)
- sin(A – B) = sin(A)cos(B) – cos(A)sin(B)
- cos(A – B) = cos(A)cos(B) + sin(u)sin(v)
- tan(A – B) = tan(A) − tan(B)/1+tan(A) tan(B)
3. If A, B and C are angles and a, b and c are the sides of a triangle, then,
Sine Laws
- a/sinA = b/sinB = c/sinC
Cosine Laws
- c2 = a2 + b2 – 2ab cos C
- a2 = b2 + c2 – 2bc cos A
- b2 = a2 + c2 – 2ac cos B
Trigonometry Formula PDF in Hindi
- ALGEBRA Handwritten Notes PDF Download
- GEOMETRY Handwritten Notes PDF Download
- Advance Maths Important Question With Solution PDF Download
- Percentage Short Tricks By Ankur Yadav Download
- Polygon Tricks By Ankur Yadav PDF Download
- Ratio and Proportion Handwritten Notes PDF Download
- Compound interest Handwritten Notes By Rajat Rajput Download
- Simple interest Tricks By Rajat Rajput PDF Download
- Trignometry Handwritten Notes By Ankur Yadav PDF Download
- Simple interest Handwritten Notes Free PDF Download
- Compound interest Handwritten Notes PDF Download
- Mathematics Handwritten Notes by Qadir rehan
- Number System by Rajat Neha Rajput PDF Download
- Profit and Loss Short Tricks Download
- Average Handwritten Notes By Ankur Yadav PDF Download
- Percentage & Number System by sulakshna kasyap Free Download
- Maths By Gyan Singh Meena Free PDF
- Complete Maths Handwritten Notes By Rehan PDF Download
- Average By Gyan Singh Meena Download
- Profit and Loss By Ankur Yadav Free Download
- Simplification Free PDF By Gyan Singh Meena
- Full handwritten Mathematics Notes Free Download
- Mihir Coaching Percentage Short Tricks PDF Download
- Time and work by Prince Download
- Train संबंधी प्रश्न Tricky Solution Free Download
- Mensuration Short Tricky Concept PDF Download
- Maths Handwritten Free Download By Sandeep Bohay
- 101 Shortcut in Mathematics PDF Download
- Algebra Class Notes Math Download
- DP SINGH Advance Maths Notes Free Download
- Alligation Short Tricks PDF Download
- Geometry Handwritten By Ankur yadav PDF Download
- Trigonometry By Devender Malik PDF Free
- Basic Calculation 500 Solved Question PDF Download
- CO-ORDINATE Geometry Notes PDF Download
- Geometry By Raj Rajesh Institute Free Download
- 1Geometry in English By Raj Rajesh Institute PDF Download
- Geometry Hand Written Notes PDF Download
- Height and Distance Tricks Download By Deep
- Algebra Tricky Notes By Puneet Sir
- Math Algebra Mayank Verma Free Download
- Rakesh Yadav Maths Notes Free Download
- Maths Without use of Pen Pencil By Sunil Kharub PDF Download
- Mensuration Handwritten Notes Free Download PDF
- Polygon and volume Handwritten Notes PDF Download
- Profit and Loss without Use of Pen and pencil PDF Download
- SS Bharti Handwritten Class Notes PDF Download
- simplification Mohit Panwar PDF Download
- 1000 Most Important Simplofication Solved Question PDF
- Algebra Formula By Mohit Panwar Free Download
- Algebra Typewise By Kunal Hooda PDF Download
- Full Arithmatic Devendra Sir PDF Download
- Simple Interest Devender Malik PDF Download
- Manvi Maths Concept Full PDF Download
- Compound Interest By Mayank Verma PDF Download
- 1Coordinate Geometry Full PDF by Mohit Chaudhary
- COORDINATE GEOMETRY By DP Singh PDF Download
- Geometry By DP Singh Free Download
- Full GEOMETRY BY DP SINGH Free Download
- Geometry Hand Written Notes By Pradeep FREE Download
- Geometry Handwritten Notes Free Download
- HCF LCM By Mohit Panwar Free Download
- Math By Sajjan Singh PDF Download
- Maths QA Short tricks PDF Download
- Number Series Solved Part 1
- 1Number Series Solved Part 2
- Number Series Solved Part 3
- Percentage Handwritten Notes Part 1
- 1Percentage Handwritten Notes Part 2
- Percentage Handwritten Notes Part 3
- Maths Short Tricks PDF Download
- Important Mathematics Solved Question PDF
- Maths Clock Tricky concept PDF Download
- Mensuration-2D Full PDF Download
- Number System Full Solved PDF Download
- Simplification Tricks PDF Free Download
- Percentage By Mayank verma PDF Download
- Profit and Loss Tricks in Hindi PDF
- Simple Interest By Mayank Verma Free Download
- Varun Mathematics Notes PDF Free Download
- Tricky Aritmetic Maths Book PDF Free Download
- Time Distance and Speed Short Tricks Concept PDF
- Mathematics Notes in English PDF Download
- SSC Advance Mathematics Full PDF Free Download
- Simplification Hand written Notes By Devendra Vmentor PDF Download
- Number System Algebra by Devender Malik
- Maths Formula PDF Free Download
- Some Imp Advance Maths Formulas in Hindi PDF
- Trigonometry Notes Formula PDF Download
Trigonometry Questions & Answers For Competitive Exams
Here we have attached some Trigonometry questions and their solutions for competitive exams like SSC, Railway, UPSC & other exams.
Question 1: In a ΔABC right angled at B if AB = 12, and BC = 5 find sin A and tan A, cos C and cot C
Solution:
AC=√((AB)^2+(BC)^2 )
=√(〖12〗^2+5^2 )
=√(144+25)
=√169=13
When we consider t-ratios of∠A we have
Base AB = 12
Perpendicular = BC = 5
Hypotenuse = AC = 13
sinA=Perpendicular/Hypotenuse=5/13
tanA=Perpendicular/Base=5/12
When we consider t-ratios of ∠C, we have
Base = BC = 5
Perpendicular = AB = 12
Hypotenuse = AC = 13
cosC = Base/Hypotenuse = 5/13
cotC = Base/Perpendicular = 5/12
Question 2 : Find the value of 2 sin2 30° tan 60° – 3 cos2 60° sec2 30°
Solution:
2(1/2)^2×√3-3(1/2)^2×(2/√3)^2
=2×1/4×√3-3×1/4×4/3=√3/2-1=(√3-2)/2
Question 3 : In a right triangle ABC right angle at B the six trigonometric ratios of ∠C
Solution:
sinA=Perpendicular/Hypotenuse=3/5
Base=√((Hypotenuse)^2-(Perpendicualr)^2 )
=√(5^2-3^2 )
=√(25-9)=√16=4
Now
sinC=BC/AC=4/5,cosecC=5/4
cosC=3/5=AB/AC,secC=5/3
tanC=AB/AC=4/3,cotC=3/4
Question 4 : Find the value of 2 sin2 30° tan 60° – 3 cos2 60° sec2 30°
Solution:
2(1/2)^2×√3-3(1/2)^2×(2/√3)^2
=2×1/4×√3-3×1/4×4/3=√3/2-1=(√3-2)/2
Question 5 : bFind the value θ sin2θ=√3
Solution:
sin2θ= √3/2
2θ = 60
θ = 30°
Question 6 : Find the value of x. Tan 3x = sin 45° cos 45° + sin 30°
Solution:
tan3x=1/√2×1/√2+1/2
=1/2+1/2=1
⇒tan3x=1 ⇒ tan3x = tan45°
3x = 45°
X = 15°
Trigonometry Problems & Solutions
Practice these questions given here to get a deep knowledge of Trigonometry. Use the formulas and table given in this article wherever necessary.
Q.1: In △ABC, right-angled at B, AB=22cm and BC=17cm. Find:
(a) sin A Cos B
(b) tan A tan B
Q.2: If 12cot θ= 15, then find sec θ?
Q.3: In Δ PQR, right-angled at Q, PR + QR = 30 cm and PQ = 10 cm. Determine the values of sin P, cos P and tan P.
Q.4: If sec 4θ = cosec (θ- 300), where 4θ is an acute angle, find the value of A.
Height And Distance
Sometimes, we have to find the height of a tower, building, tree, distance of a ship, width of a river, etc.
Though we cannot measure them easily, we can determine these by using trigonometric ratios.
Line of Sight
The line of sight or the line of vision is a straight line to the object we are viewing. If the object is above the horizontal from the eye, we have to lift up our head to view the object. In this process, our eye move, through an angle. This angle is called the angle of elevation of the object.
If the object is below the horizontal from the eye, then we have no turn our head downwards no view the object. In this process, our eye move through an angle. This angle is called the angle of depression of the object.
Example: A 25 m long ladder is placed against a vertical wall of a building. The foot of the ladder is 7m from base of the building. If the top of the ladder slips 4m, then the foot of the Ladder will slide by how much distance.
Sol: Let the height of the wall be h.
Now, h = √(〖25〗^2-7^2 )
= √(576 ) = 24m
QS = √(625-400)
= √(225 )=15m
Required distance, X = (15-7) = 8m
Trigonometry Practice Questions Worksheet PDF
Here we have attached the trigonometry practice questions pdf along with the trigonometry worksheet pdf. You can also download Complete Trigonometry Study Materials PDF from the table given below:
Trigonometry Study Materials & Worksheets PDF | Download PDF |
Trigonometry Study Materials & Formulae PDF | Download |
Trigonometry Practice Worksheet PDF | Download |
Trigonometry SSC CGL 2011 to 2018 Questions PDF | Download |
Trigonometry Frequently Asked Questions
What do you Mean by Trigonometry?
Ans. – Trigonometry is one of the branches of mathematics which deals with the relationship between the sides of a triangle (right triangle) with its angles. There are 6 trigonometric functions to define It.
What are the Different Trigonometric Functions?
Ans. – The 6 trigonometric functions are: Sine function, Cosine function, Tan function, Sec function, Cot function, Cosec function
Who is the Father of Trigonometry?
Ans. – Hipparchus was a Greek astronomer who lived between 190-120 B.C. He is considered the father of trigonometry.
What are the Applications of Trigonometry in Real Life?
Ans. – The real life applications of trigonometry is in the calculation of height and distance. Some of the sectors where the concepts of trigonometry is extensively used are aviation department, navigation, criminology, marine biology, etc.