Class 11 Exam  >  Class 11 Videos  >  Properties (Part - 11) - Trigonometric Functions, Math, Class 11

Properties (Part - 11) - Trigonometric Functions, Math, Class 11 Video Lecture

FAQs on Properties (Part - 11) - Trigonometric Functions, Math, Class 11 Video Lecture

1. What are the basic properties of trigonometric functions?
Ans. The basic properties of trigonometric functions include periodicity, amplitude, phase shift, and vertical shift. The periodicity property states that the trigonometric functions repeat their values after a certain interval. The amplitude property determines the maximum and minimum values of the function. The phase shift property indicates the horizontal displacement of the function. The vertical shift property represents the vertical displacement of the function.
2. How can I determine the period of a trigonometric function?
Ans. To determine the period of a trigonometric function, you need to find the value of the coefficient in front of the independent variable. For example, in the function y = sin(2x), the coefficient is 2. The period of the function is then calculated by dividing 2π by the coefficient, which in this case is π. Therefore, the period of the function is π.
3. What is the role of amplitude in trigonometric functions?
Ans. The amplitude of a trigonometric function determines the maximum and minimum values of the function. It represents the vertical scaling factor of the function. For example, in the function y = 3sin(x), the amplitude is 3. This means that the function will have a maximum value of 3 and a minimum value of -3. The amplitude also affects the shape and size of the graph of the trigonometric function.
4. How do I find the phase shift of a trigonometric function?
Ans. To find the phase shift of a trigonometric function, you need to determine the horizontal displacement of the function. This can be done by setting the argument of the function (inside the parentheses) equal to zero and solving for the value of x. For example, in the function y = sin(x - π/4), the phase shift is π/4. This means that the graph of the function is shifted to the right by π/4 units.
5. Can the vertical shift of a trigonometric function change its period?
Ans. No, the vertical shift of a trigonometric function does not change its period. The period of a trigonometric function is solely determined by the coefficient in front of the independent variable. The vertical shift only affects the position of the graph along the y-axis. It moves the entire graph up or down without altering the shape or size of the function.
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