sin 2pi
Understand the Problem
The question is asking for the value of the sine function at an angle of 2π radians. This involves understanding trigonometric functions and their periodic nature.
Answer
0
Answer for screen readers
The final answer is 0
Steps to Solve
- Recall the periodicity of the sine function
The sine function has a period of $2\pi$, which means $\sin(\theta) = \sin(\theta + 2k\pi)$ for any integer $k$. Therefore,
$$\sin(2\pi) = \sin(0 + 2\pi) = \sin(0)$$
- Evaluate $\sin(0)$
From the unit circle, we know that the sine of $0$ radians is $0$.
$$\sin(0) = 0$$
Therefore,
$$\sin(2\pi) = 0$$
The final answer is 0
More Information
The sine function has a periodicity of $2\pi$, so $\sin(2\pi)$ is equivalent to $\sin(0)$. Since $\sin(0) = 0$, $\sin(2\pi)$ also equals $0$.
Tips
A common mistake is to overlook the periodic nature of the sine function and not use the fact that $\sin(2\pi)$ is equivalent to $\sin(0)$.