Question

Shay created the table below to graph the equation r=2-sin theta (rounded to the hundredths place). Analyze the table. Did Shay make a mistake? If there is a mistake, which point is incorrect

Answer 1

The given equation is

$r=2-sin\theta$

To find the incorrect point, we will substitute the value of theta in each point and find the value of r to the nearest 2 decimal points and compare it with the value of r of the point

$\begin{gathered} \theta=0 \\ r=2-sin0 \\ r=2-0 \\ r=2 \end{gathered}$

Answer A is correct

$\begin{gathered} \theta=\frac{\pi}{6} \\ r=2-sin\frac{\pi}{6} \\ r=2-\frac{1}{2} \\ r=1.5 \end{gathered}$

Answer B is correct

$\begin{gathered} \theta=\frac{\pi}{3} \\ r=2-sin\frac{\pi}{3} \\ r=1.13 \end{gathered}$

Since the value of corresponding r is 2.09, then

Answer C is incorrect

The answer is C