Question

Number of solution(s) of the equation $\sin \left(\frac{5x}{2}\right)=0$ in $[0,2\pi ]$ is/are

• A. 6
• B. 06
• C. 6.00
• D. 6.0

Answer 1

Answer: (A), (B), (C), (D)

Number of solutions of the equation $\sin \left(\frac{5x}{2}\right)=0$ in $[0,2\pi ]$ is same as the number of points of intersection of $y=\sin \left(\frac{5x}{2}\right)$ and $y=0$ or x-axis
Here, the fundamental function involved is $\sin x$ whose graph is given by

Now, to obtain the graph of $y=\sin \left(\frac{5x}{2}\right)$ , we need to apply a vertical stretch by $\frac{5}{2}$units to the graph of $y=\sin x$ as shown below
Clearly, points of intesection of above graph with x-axis are 6 in $[0,2\pi ]$.
Hence, the given equation have 6 solutions