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Chapter 5 – Trigonometry

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Trigonometry is a branch of mathematics with a wide range of practical applications. Its concept was given by the Greek mathematician Hipparchus. You must have learnt basic trigonometry during your maths classes and surely must be wondering what is trigonometry and trigonometric ratios of complementary angles? Trigonometry finds its use not only in maths but also in other subjects, including science and engineering. You can even use trigonometry in solving your numerous geometrical problems without using the base geometrical concepts. This article explores the basic concept of trigonometry, which is useful for your coming exams and other competitive examinations.

Basic trigonometry deals with three fundamental ratios, namely the sine, cosine and tan ratios. These ratios correspond to the ratios of the different sides of a right-angled triangle. The whole trigonometry ratios are based on the right triangle. The basic trigonometric functions for the right-angled triangle are given below.

In the above triangle, angle B is a right angle. Hence, now we can calculate different trigonometric ratios for the above triangle.

  • Sine: Sine is the ratio of the opposite side to the hypotenuse.
  • Cosine: Cosine is the ratio of the adjacent side to the hypotenuse.
  • Tangent: Tan function is the ratio of the opposite side to the adjacent side.
  • Cosecant: Cosec is the ratio of the hypotenuse to the opposite side.
  • Secant: Sec is the ratio of the hypotenuse to the adjacent side.
  • Cotangent: Cotan is the ratio of the adjacent side to the opposite side.
RatioSide
Sine ABC/AC
Cosine AAB/AC
Tangent ABC/AB
Cotangent AAB/BC
Cosec AAC/BC
Sec AAC/AB

Some of the applications of trigonometry are given below.

  • In real-world geometry, trigonometric ratios are used to find the heights and distances from a particular point. For example, if you are seeing a huge skyscraper in front of you and want to figure out the skyscraper’s height, simply using the elevation angle and the horizontal distance between you two is enough to find the height of the skyscraper.
  • Trigonometry is extensively used in engineering and drawing subjects for building models and prototypes.
  • It is used in physics for determining various physical parameters of any machine/object.

While solving various algebraic expressions, you can easily use trigonometric identities to get to the answer quickly. As we said before, you can use trigonometric ratios for solving even traditional geometrical problems. Sine, cosine, and tangent are the three basic trigonometric identities. The rest of the identities are based on these. Hence, explore these three basic identities, and you can follow up with the rest.

Trigonometric ratios of complementary angles include the identity of two angles whose sum is 90 degrees. Therefore, if we have an angle A, then its complementary angle will be 90-A.

Trigonometry is considered an ancient mathematical tool developed during the Greek period of Hipparchus. We know that there are many great Greek mathematicians and philosophers that gave us some of the best mathematical concepts that still find their use. There are six main trigonometric functions that are used throughout the trigonometric concepts. These trigonometric functions are used in various applications such as navigation, mapping, engineering and more.

  1. What are trigonometric ratios?
    Trigonometric ratios are the ratios of sides in the right-angled triangle corresponding to a definite angle. Hence from a given reference angle, we can have six unique trigonometric ratios associated with it that can be used to find the heights and distances, including the solution to your questions.
  2. What are the three primary trigonometric ratios?
    The three basic trigonometric ratios are the sine, cosine and tangent ratios that correspond to the ratio of the different sides of the right-angled triangle. The meaning of the different trigonometric ratios is given below.
    Sine: Sine is the ratio of the opposite side to the hypotenuse.
    Cosine: Cosine is the ratio of the adjacent side to the hypotenuse.
    Tangent: Tan function is the ratio of the opposite side to the adjacent side.
  3. What are the six different trigonometric function formulas?
    The six different trigonometric function values are given as follows.
    Sine: Sine is the ratio of the opposite side to the hypotenuse.
    Cosine: Cosine is the ratio of the adjacent side to the hypotenuse.
    Tangent: Tan function is the ratio of the opposite side to the adjacent side.
    Cosecant: Cosec is the ratio of the hypotenuse to the opposite side.
    Secant: Sec is the ratio of the hypotenuse to the adjacent side.
    Cotangent: Cotan is the ratio of the adjacent side to the opposite side.
  4. What are some of the real-life applications of trigonometry?
    Some real-life applications of trigonometry include calculating heights and distances in civil engineering. It also has uses in designing models in CAD/ AUTOCAD and navigation, criminology, and more.
  5. Is there any relation between the tangent and cotangent function?
    Yes, the tangent and the cotangent function are related to each other. Cotangent is the reciprocal value of the tangent and vice-versa.

On the MSVgovideo library, you can check various applications of trigonometric ratios, including different joint identities. The intuitive video lessons deal with all the trigonometric concepts easily.

High School Physics

  • Alternating Current
  • Atoms
  • Communication Systems
  • Current Electricity
  • Dual nature of Radiation and Matter
  • Electric Charges and Fields
  • Electricity
  • Electromagnetic Induction
  • Electromagnetic Waves
  • Electron Beams and Radioactivity
  • Electrons and Photons
  • Electrostatic Potential and Capacitance
  • Fluid Pressure
  • Force and Acceleration
  • Force And Laws Of Motion
  • Gravitation
  • Internal Energy
  • Kinetic Theory
  • Law of motion
  • Light – Reflection And Refraction
  • Magnetic Effects Of Electric Current
  • Magnetism and Matter
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  • Mechanical properties of Fluids
  • Mechanical properties of Solids
  • Motion
  • Motion in a plane
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  • Moving Charges and Magnetism
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  • Nuclei
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  • Our Environment
  • Paths of Heat
  • Physical world
  • Ray optics and optical instruments
  • Semiconductor Devices
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  • Simple Machines
  • Sound
  • Sources Of Energy
  • Specific and Latent Heats
  • Spherical Mirrors
  • Static Electricity
  • Systems of Particles and Rotational motion
  • Thermal properties of matter
  • Thermodynamics
  • Units and Measurement
  • Vectors, Scalar Quantities and Elementary Calculus
  • Wave Optics
  • Waves
  • Work, Power and Energy

High School Chemistry

  • Acids, Bases and Salts
  • Alcohols, Phenols and Ethers
  • Aldehydes, Ketones and Carboxylic Acids
  • Aliphatic and Aromatic Hydrocarbons
  • Alkyl and Aryl Halides
  • Amines
  • Analytical Chemistry 
  • Atomic Structure
  • Atoms And Molecules
  • Basic concepts of Chemistry
  • Biomolecules
  • Carbon And Its Compounds
  • Carboxylic acids and Acid Derivatives
  • Chemical Bonding and Molecular Structures
  • Chemical Energetics
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  • Chemical Reactions And Equations
  • Chemical Reactions and Their Mechanisms
  • Chemistry in Everyday Life
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  • Classification of Elements
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  • The d-block and f-block elements
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  • The Solid State
  • Thermodynamics

High School Biology

  • Absorption and Movement of Water in Plants
  • Adolescent Issues
  • Anatomy of Flowering Plants
  • Animal Kingdom
  • Bacteria and Fungi-Friends and Foe
  • Biodiversity and Conservation
  • Biofertilizers
  • Biological Classification
  • Biomedical Engineering
  • Biomolecules
  • Biotechnology and its Applications
  • Biotic Community
  • Body Fluids and Circulation
  • Breathing and Exchange of Gases
  • Cell – Unit of Life
  • Cell Cycle and Cell Division
  • Cell Division and Structure of Chromosomes
  • Cell Reproduction
  • Cellular Respiration
  • Chemical Coordination and Integration
  • Circulation
  • Control And Coordination
  • Crop Improvement
  • Digestion and Absorption
  • Diversity In Living Organisms
  • Ecosystem
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  • Excretory Products and their Elimination
  • Flowering Plants
  • Genes and Chromosomes
  • Health and Diseases
  • Health and Its Significance
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  • How Do Organisms Reproduce?
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  • Neural Control And Coordination
  • Nutrition in Human Beings
  • Organism and Population
  • Photosynthesis
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  • Plant Growth and Development
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  • Principles of Inheritance and Variation
  • Reproduction and Development in Angiosperms
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  • The Nervous System and Sense Organs
  • Tissues
  • Transpiration
  • Transport in Plants

High School Math

  • Algebra – Arithmatic Progressions
  • Algebra – Complex Numbers and Quadratic Equations
  • Algebra – Linear Inequalities
  • Algebra – Pair of Linear Equations in Two Variables
  • Algebra – Polynomials
  • Algebra – Principle of Mathematical Induction
  • Algebra – Quadratic Equations
  • Binomial Theorem
  • Calculus – Applications of Derivatives
  • Calculus – Applications of the Integrals
  • Calculus – Continuity and Differentiability
  • Calculus – Differential Equations
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  • Geometry – Area
  • Geometry – Circles
  • Geometry – Conic Sections
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  • Geometry – Introduction to Euclid’s Geometry
  • Geometry – Three-dimensional Geometry
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  • Geometry – Quadrilaterals
  • Geometry – Straight Lines
  • Geometry – Triangles
  • Linear Programming
  • Matrices and Determinants
  • Mensuration – Areas
  • Mensuration – Surface Areas and Volumes
  • Number Systems
  • Number Systems – Real Numbers
  • Permutations and Combinations
  • Probability
  • Sequence and Series
  • Sets and Functions
  • Statistics 
  • Trignometry – Height and Distance
  • Trignometry – Identities
  • Trignometry – Introduction

Middle School Science

  • Acids, Bases And Salts
  • Air and Its Constituents
  • Basic Biology
  • Body Movements
  • Carbon and Its Compounds
  • Cell – Structure And Functions
  • Changes Around Us
  • Chemical Effects Of Electric Current
  • Chemistry in Your Life
  • Coal And Petroleum
  • Combustion And Flame
  • Components Of Food
  • Conservation Of Plants And Animals
  • Crop Production And Management
  • Electric Current And Its Effects
  • Electricity And Circuits
  • Elements and Compounds
  • Fibre To Fabric
  • Food production and management
  • Force And Pressure
  • Forests: Our Lifeline
  • Friction
  • Fun With Magnets
  • Garbage In, Garbage Out
  • Getting To Know Plants
  • Health and Hygiene
  • Heat
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  • Life Processes: Nutrition in Animals and Plants
  • Light, Shadows And Reflections
  • Materials: Metals And Non-Metals
  • Matter and Its States
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  • Micro Organisms: Friend And Foe
  • Motion And Measurement Of Distances
  • Motion And Time
  • Nutrition In Animals
  • Nutrition In Plants
  • Organization in Living Things
  • Our Environment
  • Physical And Chemical Changes
  • Pollution and conservation
  • Pollution Of Air And Water
  • Reaching The Age Of Adolescence
  • Reproduction In Animals
  • Reproduction In Plants
  • Respiration In Organisms
  • Rocks and Minerals
  • Separation Of Substances
  • Simple Machines
  • Soil
  • Some Natural Phenomena
  • Sorting Materials Into Groups
  • Sound
  • Stars And The Solar System
  • Structure of Atom
  • Synthetic Fibers And Plastics
  • The Living Organisms And Their Surroundings
  • Transfer of Heat
  • Transformation of Substances
  • Transportation In Animals And Plants
  • Universe
  • Waste-water Story
  • Water: A Precious Resource
  • Weather, Climate And Adaptations Of Animals To Climate
  • Winds, Storms And Cyclones

Middle School Math

  • Addition
  • Area and Its Boundary
  • Boxes and Sketches
  • Data Handling
  • Fun With Numbers
  • Heavy and Light
  • How Many
  • Long And Short
  • Mapping
  • Measurement
  • Money
  • Multiplication and Factors
  • Multiply and Divide
  • Numbers
  • Parts and Wholes
  • Pattern Recognition
  • Patterns
  • Play With Patterns
  • Rupees And Paise
  • Shapes And Angles
  • Shapes And Designs
  • Shapes and Space
  • Similarity
  • Smart Charts
  • Squares
  • Subtraction
  • Tables And Shares
  • Tenths and Hundredths
  • Time
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