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Trigonometric Ratios- 1 Video Lecture - Class 10
FAQs on Trigonometric Ratios- 1 Video Lecture - Class 10
| 1. What are trigonometric ratios? |  |
Ans. Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides. The three main trigonometric ratios are sine (sin), cosine (cos), and tangent (tan), which are defined as the ratios of the lengths of the sides in relation to a given angle.
| 2. How do you calculate trigonometric ratios? | |
Ans. To calculate the trigonometric ratios, you need to have a right triangle with one angle known. For example, to find the sine of an angle, divide the length of the side opposite the angle by the length of the hypotenuse. Similarly, the cosine is found by dividing the length of the adjacent side by the length of the hypotenuse, and the tangent is found by dividing the length of the opposite side by the length of the adjacent side.
| 3. What is the range of trigonometric ratios? | |
Ans. The range of trigonometric ratios is always between -1 and 1, inclusive. For example, the sine and cosine ratios can never be greater than 1 or less than -1, as they represent the ratios of lengths of sides, which are always smaller than or equal to the hypotenuse.
| 4. How are trigonometric ratios used in real life? | |
Ans. Trigonometric ratios have numerous applications in various fields. They are used in navigation and surveying to determine distances and angles, in physics to analyze oscillatory motion and waves, in engineering to design structures and calculate forces, and in astronomy to study celestial objects and their movements.
| 5. What is the Pythagorean identity related to trigonometric ratios? | |
Ans. The Pythagorean identity is a fundamental trigonometric identity that relates the three main trigonometric ratios. It states that for any angle in a right triangle, the square of the sine of the angle plus the square of the cosine of the angle is always equal to 1. This identity is expressed as sin²θ + cos²θ = 1, where θ represents the angle in the triangle.
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