Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  Facts that Matter: Introduction to Trigonometry

Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10 PDF Download

Trigonometric Ratios

The certain ratios involving the sides of a right-angled triangle are called trigonometric ratios. Look at the adjoining right triangle ABC, right-angled at B. The Trigonometric Ratios of angle A are:
Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10
Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10
Reciprocals of the above T-ratios are:
Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10
Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10
Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10

NOTE:
I. ‘sin θ ’ is a single symbol and ‘sin’ cannot be detached from ‘θ ’. sin θ ≠ sin × θ. This remark is true for other t-ratios also.
II. The values of the trigonometric ratios of an angle depend only on the magnitude of the angle and not on the lengths of the sides of the triangle.
III. In a right angle, the hypotenuse is the longest side, therefore, the value of sin A or cos A is always less than 1 or at the most equal to 1.

Trigonometric Ratios of Some Specific Angles 

The specific angles are 0°, 30°, 45°, 60° and 90°. Trigonometric ratios of these angles are given in the following table:

Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10

NOTE:
I. The value of sin A increases from 0 to 1, as A increases from 0° to 90°.
II. The value of cos A decreases from 1 to 0, as A increases from 0° to 90°.
III. The value of tan A increases from 0 to ∞ , as A increases from 0° to 90°.
IV. √2 = 1.414 and √3 = 1.732.

Trigonometric Identities 

Since an equation is called an identity when it is true for all the values of the variables involved.

So, an equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angles involved. Some of the useful trigonometric identities:

(i) cos2A + sin2A = 1

(ii) 1 + tan2A = sec2A

(iii) cot2A + 1 = cosec2A

The document Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10
120 videos|463 docs|105 tests

FAQs on Facts that Matter: Introduction to Trigonometry - Mathematics (Maths) Class 10

1. What are trigonometric ratios?
Ans. Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratio of the lengths of its sides. The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).
2. How can trigonometric ratios be used to find missing side lengths in a right triangle?
Ans. Trigonometric ratios can be used to find missing side lengths in a right triangle through the use of inverse trigonometric functions. For example, if we know the angle and one side length, we can use the sine function to find the length of another side.
3. What are the trigonometric ratios for the angles 0°, 30°, 45°, 60°, and 90°?
Ans. The trigonometric ratios for the angles 0°, 30°, 45°, 60°, and 90° are as follows: - For 0°: sin(0°) = 0, cos(0°) = 1, tan(0°) = 0. - For 30°: sin(30°) = 1/2, cos(30°) = √3/2, tan(30°) = √3/3. - For 45°: sin(45°) = √2/2, cos(45°) = √2/2, tan(45°) = 1. - For 60°: sin(60°) = √3/2, cos(60°) = 1/2, tan(60°) = √3. - For 90°: sin(90°) = 1, cos(90°) = 0, tan(90°) = undefined.
4. Can trigonometric ratios be negative?
Ans. Yes, trigonometric ratios can be negative. The sign of a trigonometric ratio depends on the quadrant in which the angle is located. In the first quadrant, all trigonometric ratios are positive. In the second quadrant, only the sine ratio is positive. In the third quadrant, only the tangent ratio is positive. In the fourth quadrant, only the cosine ratio is positive.
5. How are trigonometric ratios used in real-life applications?
Ans. Trigonometric ratios have various applications in real life, including: - Navigation and GPS systems use trigonometry to calculate distances and angles. - Architects and engineers use trigonometry to design and construct buildings, bridges, and other structures. - Astronomers use trigonometry to study celestial objects and calculate distances between them. - Trigonometry is used in physics and engineering to analyze and model periodic phenomena, such as waves and vibrations. - Trigonometry is also applied in fields like computer graphics, music, and biology.
120 videos|463 docs|105 tests
Download as PDF
Explore Courses for Class 10 exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Download the FREE EduRev App
Track your progress, build streaks, highlight & save important lessons and more!
Related Searches

Summary

,

Important questions

,

Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10

,

MCQs

,

video lectures

,

Objective type Questions

,

practice quizzes

,

Previous Year Questions with Solutions

,

Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10

,

Sample Paper

,

Exam

,

shortcuts and tricks

,

mock tests for examination

,

pdf

,

Viva Questions

,

Semester Notes

,

ppt

,

past year papers

,

Facts that Matter: Introduction to Trigonometry | Mathematics (Maths) Class 10

,

Free

,

study material

,

Extra Questions

;