#### My x **values** are **between 0 and 1**, and i would like this function to behave exponentially, so that only x **values** close to **1** have y **values** close to **1** (and vice versa x **values** close to **0** have y **values** close to **0**). The function should behave asymptotically, so that: $\lim_{x \rightarrow **1**} f(x) = **1**$ and $\lim_{x \rightarrow **0**} f(x) = **0**$. The **sine** function produces results **between** - **1 and 1** , but you want to go **between 0 and 1** . To scale it properly you want (**sin** (x)+**1**)/2. The **sine** function starts at zero, goes to **1** at pi/2, zero again at pi, - **1** at 3*pi/2, and back to zero at 2*pi. Scaled, the first zero will happen at 3*pi/2 and the first maximum after that will be at 5/2*pi. Confirm by looking at the graph above, and zooming in if necessary (shift + scroll wheel), that indeed, it appears that. lim. θ→**0**. **sin** ( θ) θ. = **1**. Now check the box next to "Show squeezing functions." Again, confirm by examining the graph above that it appears that. cos 2 ( θ) <.

**sine**of an angle is equal to the height of the point on the unit circle given the correct angle, and since the unit circle reaches only heights

**between**−

**1 and 1**, so does the

**sine**function. For your other question, the answer is fairly simple. The unit circle can be defined as the set. Figure

**1**.

**The Sine Bar**. Two cylinders of equal diameter are placed at the ends of the bar. The axes of these two cylinders are mutually parallel to each other, and are also parallel to, and at equal distance from, the upper surface of

**the sine bar**. Accuracy up to

**0**.01mm/m of length of

**the sine bar**can be obtained. x = float ( input ("Enter the number ( 0-1 ) = ")) print ( math .sin (x)) In the above program, Firstly the math module is imported for accessing the function of

**sine**pre-defined in it. After that, the input is taken into the variable ' x '. And Finally, the print statement is used to print the

**value**

**of**the

**sine**

**value**

**of**the inputted

**value**

**of**.