Wite the finction of the form $$ y= $$ sin bx corresponding to the guen period. Penod 1 Fill in the correct value for b. $$ y=\sin (\square x) $$ (Type an exact answer in lerms of $$ \pi $$. Use intepers or fractions for any numbers in the exprescion Simplity your anower)

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To determine the function of the form $$ y = \sin(bx) $$ with a given period, we can use the relationship between the period $$ T $$ and the coefficient $$ b $$ in the sine function.

### Step-by-Step Solution:

1. **Understand the Formula:**
   The period $$ T $$ of the sine function $$ y = \sin(bx) $$ is given by:
   $$
   T = \frac{2\pi}{|b|}
   $$

2. **Given Period:**
   You mentioned the period $$ T $$ is **1**.

3. **Solve for $$ b $$:**
   $$
   1 = \frac{2\pi}{|b|}
   $$
   $$
   |b| = 2\pi
   $$
   Since $$ b $$ can be positive or negative and the sine function is periodic, we can take $$ b $$ as positive for simplicity:
   $$
   b = 2\pi
   $$

4. **Write the Function:**
   Substituting $$ b = 2\pi $$ into the sine function:
   $$
   y = \sin(2\pi x)
   $$

### Final Answer:
$$
y = \sin(2\pi\,x)
$$
$$ y = \sin(2\pi x) $$

Wite the finction of the form sin bx corresponding to the guen period.
Penod 1
Fill in the correct value for b.

(Type an exact answer in lerms of . Use intepers or fractions for any numbers in the exprescion Simplity your anower)

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Wite the finction of the form sin bx corresponding to the guen period. Penod 1 Fill in the correct value for b. (Type an exact answer in lerms of . Use intepers or fractions for any numbers in the exprescion Simplity your anower)