graph (f(\theta)=-cos(2pi\theta)) where (0leq\thetaleq1). state the period of the function.

Answer

Explanation:

Step1: Recall period - formula for cosine function

The general form of a cosine function is $y = A\cos(Bx - C)+D$, and its period is given by $T=\frac{2\pi}{|B|}$. For the function $f(\theta)=-\cos(2\pi\theta)$, we have $B = 2\pi$.

Step2: Calculate the period

Substitute $B = 2\pi$ into the period - formula $T=\frac{2\pi}{|B|}$. Then $T=\frac{2\pi}{|2\pi|}=1$.

To graph the function $y =-\cos(2\pi\theta)$ for $0\leq\theta\leq1$:

When $\theta = 0$, $y=-\cos(0)=- 1$.
When $\theta=\frac{1}{4}$, $y =-\cos(\frac{\pi}{2}) = 0$.
When $\theta=\frac{1}{2}$, $y=-\cos(\pi)=1$.
When $\theta=\frac{3}{4}$, $y =-\cos(\frac{3\pi}{2}) = 0$.
When $\theta = 1$, $y=-\cos(2\pi)=-1$.

The graph of $y =-\cos(2\pi\theta)$ is a cosine - shaped curve that is reflected about the $x$ - axis (due to the negative sign in front of the cosine function) and has a period of 1.

Answer:

The period of the function $f(\theta)=-\cos(2\pi\theta)$ is 1.