Chapter 9.2, Problem 38E

To determine

To find: the four pairs of polar coordinates that represent the same point as $\left(4,{45}^{\circ }\right)$ .

Answer to Problem 38E

The pairs are $\left(4,{395}^{\circ }\right),\left(4,{765}^{\circ }\right),\left(4,{1125}^{\circ }\right),\left(4,{1485}^{\circ }\right)$ .

Explanation of Solution

Given information:

The point is $\left(4,{45}^{\circ }\right)$ .

Calculation: to find the other pairs, change the value of $\theta$ , add the multiplicative of ${360}^{\circ }$ to get the same point as $\left(4,{45}^{\circ }\right)$ .

Thus, the other pairs are $\left(4,{395}^{\circ }\right),\left(4,{765}^{\circ }\right),\left(4,{1125}^{\circ }\right),\left(4,{1485}^{\circ }\right)$ .