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FAQs on INTRO TO TRIGONOMETRY - Class 10
| 1. What is trigonometry? |  |
Ans. Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It involves the study of trigonometric functions such as sine, cosine, and tangent, which are used to solve various problems related to angles and distances.
| 2. What are the basic trigonometric ratios? | |
Ans. The basic trigonometric ratios are sine, cosine, and tangent. These ratios are defined as follows:
- Sine (sin): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
- Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse.
- Tangent (tan): The ratio of the length of the side opposite the angle to the length of the adjacent side.
These ratios are fundamental in trigonometry and are used to calculate unknown angles or side lengths in a triangle.
| 3. How are trigonometric ratios used in real-life applications? | |
Ans. Trigonometric ratios have various applications in real-life scenarios. Some examples include:
- Architecture and Engineering: Trigonometry is used to calculate the angles and distances in building structures, bridges, and other architectural designs.
- Astronomy and Navigation: Trigonometry helps in determining the positions of celestial objects, calculating distances between stars and planets, and navigating ships or aircraft.
- Physics and Engineering: Trigonometry is used to analyze the motion of objects, such as projectile motion and harmonic motion.
- Geometry and Land Surveying: Trigonometry is applied in measuring land areas, determining heights of buildings or mountains, and creating accurate maps.
| 4. What is the unit circle in trigonometry? | |
Ans. The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. In trigonometry, the unit circle is used to define the values of trigonometric functions for all angles, including those beyond 90 degrees or 180 degrees. The coordinates of points on the unit circle correspond to the values of sine and cosine for different angles.
| 5. How can I use trigonometry to solve triangles? | |
Ans. Trigonometry can be used to solve triangles by using the trigonometric ratios and the laws of sines and cosines. To solve a triangle, you need to know at least three of its side lengths or angles. By applying the appropriate trigonometric ratios and formulas, you can find the missing angles or side lengths of the triangle.
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