Which of the following statements is correcta)The function y = sinx is...
The correct statement is option D: The function y = tanx is periodic with period π.
- Periodic Function: A function is said to be periodic if it repeats its values at regular intervals. In other words, a function f(x) is periodic if there exists a positive number p such that f(x + p) = f(x) for all x.
Explanation:
1. The function y = sinx is periodic with period 2π.
- The sine function repeats its values every 2π radians or 360 degrees. Therefore, the correct statement is not option A.
2. The function y = cosecx is not periodic with period π/2.
- The cosecant function, csc(x), is the reciprocal of the sine function, 1/sinx. Since the sine function has a period of 2π, the cosecant function also has a period of 2π. Therefore, the correct statement is not option B.
3. The function y = cosx is periodic with period 2π.
- The cosine function also repeats its values every 2π radians or 360 degrees. Therefore, the correct statement is not option C.
4. The function y = tanx is periodic with period π.
- The tangent function repeats its values every π radians or 180 degrees. This can be seen from the graph of the tangent function, which has vertical asymptotes at x = (n + 1/2)π, where n is an integer. Between these asymptotes, the tangent function repeats its values. Therefore, the correct statement is option D.
Summary:
- The function y = tanx is periodic with period π.
Which of the following statements is correcta)The function y = sinx is...
I think a and d both options are correct
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