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Trigonometric Functions & the Unit Circle Video Lecture | Quantitative Aptitude (Quant) - CAT

185 videos|158 docs|113 tests

FAQs on Trigonometric Functions & the Unit Circle Video Lecture - Quantitative Aptitude (Quant) - CAT

1. What are the trigonometric functions?
Ans. Trigonometric functions are mathematical functions that relate angles to the ratios of the sides of a right triangle. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions are widely used in various fields such as physics, engineering, and geometry to study the properties of angles and triangles.
2. 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 any angle. The coordinates of a point on the unit circle correspond to the cosine and sine values of the angle formed between the positive x-axis and the line connecting the origin to that point.
3. How do trigonometric functions relate to the unit circle?
Ans. The values of trigonometric functions such as sine and cosine can be determined by considering the coordinates of a point on the unit circle. For any angle θ, the coordinates (cosθ, sinθ) of the corresponding point on the unit circle give the values of cosine and sine, respectively. This relationship allows us to easily calculate the trigonometric values for various angles using the unit circle.
4. What is the purpose of using the unit circle in trigonometry?
Ans. The unit circle provides a visual representation of the trigonometric functions and their values for any angle. It helps in understanding the periodicity, symmetry, and relationships between the trigonometric functions. The unit circle also simplifies calculations involving trigonometric functions by providing a reference point for determining the values of sine and cosine.
5. How can the unit circle be used to solve trigonometric equations?
Ans. Trigonometric equations involve solving for unknown angles or trigonometric values. The unit circle can be used to find solutions to these equations by considering the coordinates of points on the unit circle that satisfy the given equation. By relating the angles on the unit circle to the values of trigonometric functions, one can determine the solutions to the trigonometric equations.
185 videos|158 docs|113 tests
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