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Important Definitions & Formulas: Introduction to Trigonometry
Definitions and Formulas
- An angle is positive if it is measured in the anticlockwise direction and negative if it is measured in the clockwise direction.
- In a right triangle ABC, right-angled at B
Reciprocal Relations
- If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios can be determined.
- Two angles are said to be complementary if their sum is 90°, and each one of them is called the complement of the other.
sin (90° - θ) = cos θ
cos (90° - θ) = sin θ
tan (90° - θ) = cot θ
cot (90° - θ) = tan θ
sec (90° - θ) = cosec θ
cosec (90° - θ) = sec θ
Try yourself: If the sine of an acute angle is known to be 0.6, what is the value of cos of the angle?MULTIPLE CHOICE QUESTION
Trigonometric Ratios of Some Specific Angles
Trigonometric Identities
An equation with trigonometric ratios of an angle θ, which is true for all values of 'θ', for which the given trigonometric ratios are defined, is called an identity.
Three fundamental trigonometric identities are
(a) sin2θ + cos2θ = 1
(b) sec2θ = 1 + tan2θ
(c) cosec2θ = 1 + cot2θ
The document Important Definitions & Formulas: Introduction to Trigonometry is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Important Definitions & Formulas: Introduction to Trigonometry
| 1. What's the difference between sine, cosine, and tangent in trigonometry? |  |
Ans. Sine, cosine, and tangent are three primary trigonometric ratios used to relate angles with sides of a right-angled triangle. Sine equals opposite/hypotenuse, cosine equals adjacent/hypotenuse, and tangent equals opposite/adjacent. These fundamental ratios form the foundation of trigonometric calculations and are essential for solving angle and side problems in Class 10 mathematics.
| 2. How do I remember sin, cos, and tan formulas for CBSE exams? | |
Ans. The memory aid "SOH-CAH-TOA" helps retain these trigonometric identities: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. Students can also use flashcards and mind maps from EduRev to visualize right triangles with labelled sides, reinforcing these trigonometric definitions through repetition and visual learning before board examinations.
| 3. What are trigonometric ratios for standard angles like 30, 45, and 60 degrees? | |
Ans. Standard angle trigonometric values are fixed: sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3; sin 45° = cos 45° = 1/√2, tan 45° = 1; sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3. These special angle values appear frequently in Class 10 mathematics problems and must be memorized for quick problem-solving during exams.
| 4. Why do we use trigonometry in real-life problems like heights and distances? | |
Ans. Trigonometry calculates unknown heights, distances, and angles using only a few known measurements-making it invaluable for architecture, surveying, and navigation. Real-world applications include finding building heights using angle of elevation, calculating distances across rivers, and determining object positions. This practical relevance explains why trigonometric applications dominate Class 10 examination question papers.
| 5. What's the connection between angles of elevation and depression in trigonometry problems? | |
Ans. Angles of elevation and depression are complementary concepts in trigonometric applications: elevation measures upward angles from horizontal sight lines, while depression measures downward angles. Both use identical trigonometric ratios to solve problems but from different observer positions. Understanding this relationship helps students correctly identify which ratio applies in height-distance problems, a common source of errors in Class 10 mathematics assessments.
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