Question

Match the graph with the polar equation

$\theta =\frac{3\pi }{4}$

Short answer

Option D is correct

Step-by-step solution

Step 1. The given information is

$\theta =\frac{3\pi }{4}$

Step 2. Transforming the given polar equation, we get

$\tan \left(\frac{3\pi }{4}\right)=-1$

Since $\tan \theta =\frac{y}{x}$

Hence,$\frac{y}{x}=-1$

Step 3. Solving we get

$$\begin{gathered} \frac{y}{x}=-1 \\ y=-x \end{gathered}$$

It is the rectangular form of the equation$\theta =\frac{3\pi }{4}$

Making the graph we get,