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L20 : Problems-2 - Trigonometry Functions, Mathematics, Class 11 Video Lecture

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FAQs on L20 : Problems-2 - Trigonometry Functions, Mathematics, Class 11 Video Lecture

1. What are the fundamental trigonometric functions?
Ans. The fundamental trigonometric functions are sine, cosine, and tangent. These functions relate the angles of a right triangle to the ratios of its sides. Sine (sin) is the ratio of the length of the side opposite the angle to the hypotenuse, cosine (cos) is the ratio of the length of the adjacent side to the hypotenuse, and tangent (tan) is the ratio of the length of the side opposite the angle to the length of the adjacent side.
2. How do trigonometric functions help in solving real-life problems?
Ans. Trigonometric functions are widely used in various fields such as engineering, physics, and architecture to solve real-life problems. They help in determining distances, heights, angles, and forces. For example, trigonometric functions can be used to calculate the height of a building, the distance between two points, the angle of elevation of a hill, or the force required to move an object.
3. What is the unit circle and how is it related to trigonometric functions?
Ans. The unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. It is used to understand the values of trigonometric functions for any angle. The coordinates of points on the unit circle correspond to the values of sine and cosine functions for different angles. For example, the point (cosθ, sinθ) on the unit circle represents the values of cosine and sine functions for the angle θ.
4. Can trigonometric functions be negative?
Ans. Yes, trigonometric functions can be negative. The signs of trigonometric functions depend on the quadrant in which the angle lies. In the first and second quadrants, all trigonometric functions are positive. In the third quadrant, only tangent is positive, and in the fourth quadrant, only cosine is positive. Sine is positive in the first and second quadrants and negative in the third and fourth quadrants.
5. How are trigonometric functions used in triangles other than right triangles?
Ans. Trigonometric functions can also be used in triangles that are not right triangles. In such cases, the Law of Sines and the Law of Cosines are used to solve for unknown angles and sides. The Law of Sines relates the ratios of the sides to the sines of the opposite angles, while the Law of Cosines relates the sides to the cosine of one of the angles. These laws allow us to find missing angles and sides in any triangle.
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