Subjects trigonometry

Period Sin Cos E67E3D

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1. **State the problem:** We need to find the period of the functions $y = \sin(x)$ and $y = \cos(x)$. Both are trigonometric functions with well-known periodic behavior. 2. **Recall the formula for the period of sine and cosine:** The general form of sine and cosine functions is $y = \sin(bx)$ or $y = \cos(bx)$, where the period is given by: $$\text{Period} = \frac{2\pi}{|b|}$$ For the standard sine and cosine functions, $b = 1$. 3. **Apply the formula:** Since $b = 1$ for both $\sin(x)$ and $\cos(x)$, their period is: $$\text{Period} = \frac{2\pi}{1} = 2\pi$$ 4. **Interpretation:** This means the sine and cosine functions repeat their values every $2\pi$ units along the x-axis. 5. **Answer:** The period of both $y = \sin(x)$ and $y = \cos(x)$ is $2\pi$. Thus, the correct choice is **2Pi**.