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    Introduction to Trigonometry Class 10th Notes - Free NCERT Class 10 Maths Chapter 8 Notes - Download PDF

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    Introduction to Trigonometry Class 10th Notes - Free NCERT Class 10 Maths Chapter 8 Notes - Download PDF

    Edited By Safeer PP | Updated on Jul 29, 2022 04:25 PM IST

    NCERT Class 10 Maths Chapter 8 Notes based on the introduction to trigonometry, in which trigonometric identities and ratios were used to find the angles and their measurement. The chapter Introduction to Trigonometry Class 10 notes also includes trigonometry ratios to be learned by students. CBSE Class 10 Maths chapter 8 notes contain systematic explanations of topics using examples and exercises. Class 10 Maths chapter 8 notes include FAQ or frequently asked questions about the chapter. All these topics can be easily downloaded from Class 10 Maths chapter 8 notes pdf download.

    Also, students can refer,

    NCERT Class 10 Chapter 1 Notes

    Introduction to Trigonometry Class 10 Notes- Topic 1:

    Trigonometry can be defined as the science of relationships between sides and right-angle triangles.

    Trigonometry Ratios: Trigonometry ratios can be defined as ratios of sides of triangles and are right-angle triangles. Let’s take an example to understand the concepts of trigonometry more clearly. Taking a right-angled triangle, In this, the ratios can be defined according to an acute angle. If one trigonometric ratio of an acute angle is known then we can easily define the other ratios.

    Trigonometric Ratios:

    The trigonometric ratios can be calculated with the help of a right-angled triangle.

    1644383926540

    Sin A=opposite side/hypotenuse=BC/AB

    Cos A=adjacent side/hypotenuse=AC/AB

    Tan A=opposite sidea/djacent side=BC/AC

    CosecA=hypotenuse/opposite side=AB/BC

    SecA=hypotenuse/adjacent side=AB/AC

    CotA=adjacent side/opposite side=AC/BC

    Trigonometric Formulas:

    tan A=sinA/cosA

    cot A=CosA/sinA=1/tanA

    SecA=1/cosA

    cosecA=1/sinA

    sin2A+cos2A=1

    sec2A-tan2A=1

    cosec2A-cot2A=1

    Trigonometric Ratios of Some Angles:

    \angle A

    0^o

    30^o

    45^o

    60^o

    90^o

    Sin A

    0

    \frac{1}{2}

    \frac{1}{\sqrt{2}}

    \frac{\sqrt{3}}{2}

    1

    Cos A

    1

    \frac{\sqrt{3}}{2}


    \frac{1}{2}

    0

    Tan A

    0

    \frac{1}{\sqrt{3}}

    1

    \sqrt{3}

    Not defined

    Cosec A

    Not defined

    2

    \sqrt{2}

    \frac{2}{\sqrt{3}}

    1

    Sec A

    1

    \frac{2}{\sqrt{3}}

    \sqrt{2}

    2

    Not defined

    Cot A

    Not defined

    \sqrt{3}

    1

    \frac{1}{\sqrt{3}}

    0

    Trigonometric Ratios of Complementary Angles:

    Complementary angles are those angles whose sum is taken out as 90 degrees.

    In the case of a right angles triangle, it can be noted that one angle is 90 degrees and in that case, the sum of the other two will be 90 degrees.

    Trigonometric ratios for complementary angle will be:

    Sin(90°-A) = Cos A

    Cos(90°-A) = Sin A

    Tan(90°-A) = Cot A

    Cot(90°-A) = Tan A

    Sec(90°-A) = Cosec A

    Cosec(90°-A) = Sec A

    Trigonometric identities with respect to Pythagoras theorem:

    1644383926350

    According to Pythagoras theorem, in the right-angled triangle at C so for triangle ABC,

    (perpendicular)2+(base)2=(hypotenuse)2

    (sin2R)+(cos2R)=1

    1+(tan2R)=sec2R

    1+(cot2R)=cosec2R

    Significance of NCERT Class 10 Maths Chapter 8 Notes

    Introduction to Trigonometry NCERT notes for Class 10 Maths chapter 8 will help to understand the formulas, statements, rules in detail. Class 10 Maths chapter 8 notes also contain previous year’s questions and NCERT TextBook pdf. Class 10 Introduction to Trigonometry contains identities, ratios, formulas, and a fixed angle table for trigonometric quantities and properties of trigonometry.

    Examples-

    1. Calculate the maximum value of 1/secθ where 0°≤θ≤90°.

    The maximum value is at 0° when we put this value get,

    =1/secθ=1/1=1

    1. Calculate the value when sin=cos, now as per this find value 2tan+cos2.

    Given that: sinθ=cosθ

    These values are equal to each other at an angle of 45 degrees.

    So

    Now, 2tanθ+cos2θ=2tan45°+cos245°

    =2(1)+ (1√2)2

    = 2+1/2=5/2

    1. Evaluate the following (1-2cot245°)/(1+sin290°)

    (1-cot245°)/(1+sin290°) =(1-1)/(1+sin290°)=0

    1. Calculate sin219°+sin271° as per formulas given in notes for Class 10 Maths chapter 8

    sin219°+sin271°=sin219°+sin2(90°-19°)

    =sin219°+cos219°=1

    1. When an increase in value of cos from 0 to 90 degrees what type of change can be observed?

    cos0°=1 , cos90°=0. When the value of the angle increases from 0 to 90 the value will decrease.

    Class 10 Chapter Wise Notes

    NCERT Solutions of Cass 10 Subject Wise

    NCERT Class 10 Exemplar Solutions for Other Subjects:

    Frequently Asked Question (FAQs)

    1. Is trigonometry an important chapter for CBSE board exam?

    Yes, the NCERT Book Class 10  Chapter Introduction To Trigonometris an important chapter of NCERT Class 10 Maths Syllabus. 8 to 10 marks questions can be expected from Trigonometry Class 10 Chapter for CBSE board exam

    2. What is the value of sin 25.cosec25?

    cosec 25=1/sin25 therefore the value of sin 25.cosec25=1

    3. Given the value of sin in first quadrant as 0. What is the value of cos in the same quadrant?

    sin =0 for 0 degrees. And cos0=1.

    4. What is sinA.SecA

    sinA.secA=sinA/cosA=tanA

    5. Find the value of sin30.cos60

    sin30=0.5


    cos60=0.5


    sin30.cos60=0.25

    Articles

    Get answers from students and experts

    A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

    Option 1)

    0.34\; J

    Option 2)

    0.16\; J

    Option 3)

    1.00\; J

    Option 4)

    0.67\; J

    A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

    Option 1)

    2.45×10−3 kg

    Option 2)

     6.45×10−3 kg

    Option 3)

     9.89×10−3 kg

    Option 4)

    12.89×10−3 kg

     

    An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

    Option 1)

    2,000 \; J - 5,000\; J

    Option 2)

    200 \, \, J - 500 \, \, J

    Option 3)

    2\times 10^{5}J-3\times 10^{5}J

    Option 4)

    20,000 \, \, J - 50,000 \, \, J

    A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

    Option 1)

    K/2\,

    Option 2)

    \; K\;

    Option 3)

    zero\;

    Option 4)

    K/4

    In the reaction,

    2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

    Option 1)

    11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

    Option 2)

    6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

    Option 3)

    33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

    Option 4)

    67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

    How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

    Option 1)

    0.02

    Option 2)

    3.125 × 10-2

    Option 3)

    1.25 × 10-2

    Option 4)

    2.5 × 10-2

    If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

    Option 1)

    decrease twice

    Option 2)

    increase two fold

    Option 3)

    remain unchanged

    Option 4)

    be a function of the molecular mass of the substance.

    With increase of temperature, which of these changes?

    Option 1)

    Molality

    Option 2)

    Weight fraction of solute

    Option 3)

    Fraction of solute present in water

    Option 4)

    Mole fraction.

    Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

    Option 1)

    twice that in 60 g carbon

    Option 2)

    6.023 × 1022

    Option 3)

    half that in 8 g He

    Option 4)

    558.5 × 6.023 × 1023

    A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

    Option 1)

    less than 3

    Option 2)

    more than 3 but less than 6

    Option 3)

    more than 6 but less than 9

    Option 4)

    more than 9

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    Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

    3 Jobs Available
    Fashion Journalist

    Fashion journalism involves performing research and writing about the most recent fashion trends. Journalists obtain this knowledge by collaborating with stylists, conducting interviews with fashion designers, and attending fashion shows, photoshoots, and conferences. A fashion Journalist  job is to write copy for trade and advertisement journals, fashion magazines, newspapers, and online fashion forums about style and fashion.

    2 Jobs Available
    Multimedia Specialist

    A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications. 

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    Corporate Executive

    Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

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    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

    3 Jobs Available
    Quality Controller

    A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

    A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

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    Production Manager

    Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers. 

    Resource Links for Online MBA 

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    QA Manager

    Quality Assurance Manager Job Description: A QA Manager is an administrative professional responsible for overseeing the activity of the QA department and staff. It involves developing, implementing and maintaining a system that is qualified and reliable for testing to meet specifications of products of organisations as well as development processes. 

    2 Jobs Available
    QA Lead

    A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans. 

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    Reliability Engineer

    Are you searching for a Reliability Engineer job description? A Reliability Engineer is responsible for ensuring long lasting and high quality products. He or she ensures that materials, manufacturing equipment, components and processes are error free. A Reliability Engineer role comes with the responsibility of minimising risks and effectiveness of processes and equipment. 

    2 Jobs Available
    Safety Manager

    A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

    2 Jobs Available
    Corporate Executive

    Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

    2 Jobs Available
    Computer Programmer

    Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

    3 Jobs Available
    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

    3 Jobs Available
    ITSM Manager

    ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks. 

    3 Jobs Available
    Information Security Manager

    Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

    3 Jobs Available
    Big Data Analytics Engineer

    Big Data Analytics Engineer Job Description: A Big Data Analytics Engineer is responsible for collecting data from various sources. He or she has to sort the organised and chaotic data to find out patterns. The role of Big Data Engineer involves converting messy information into useful data that is clean, accurate and actionable. 

    2 Jobs Available
    Cloud Solution Developer

    A Cloud Solutions Developer is basically a Software Engineer with specialisation in cloud computing. He or she possesses a solid understanding of cloud systems including their operations, deployment with security and efficiency with no little downtime. 

    2 Jobs Available
    CRM Technology Consultant

    A Customer Relationship Management Technology Consultant or CRM Technology Consultant is responsible for monitoring and providing strategy for performance improvement with logged calls, performance metrics and revenue metrics. His or her role involves accessing data for team meetings, goal setting analytics as well as reporting to executives.  

    2 Jobs Available
    IT Manager

    Career as IT Manager  requires managing the various aspects of an organization's information technology systems. He or she is responsible for increasing productivity and solving problems related to software and hardware. While this role is typically one of the lower-level positions within an organisation, it comes with responsibilities related to people and ownership of systems.

    2 Jobs Available
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