Question

Which point represents the polar coordinates (6, 30)?

A. (5.2, 3)
B. (5.3, 2)
C. (3, 5.2)
D. (3.2, 5)

Answer 1

Which point represents the polar coordinates (6, 30)?

A. (5.2, 3)

B. (5.3, 2)

C. (3, 5.2)

D. (3.2, 5)

**Solution:**

Polar coordinates are $(r,\theta)$. Rectangular coordinates are $(x,y)$. Conversion from polar to rectangular coordinates is

$$x = r * \cos (\theta)$$ $$y = r * \sin (\theta)$$

In our case $r = 6$, and $\theta = 30{}^\circ$

$$x = 6 * \cos(30) = 6 * \frac{\sqrt{3}}{2} = 5.2$$ $$y = 6 * \sin(30) = 6 * \frac{1}{2} = 3$$

So in Rectangular coordinates it is point (5.2,3).

**Answer:** A (5.2, 3)