Chapter 5.1, Problem 64E

To determine

To write: An expression that represents any angle that is coterminal with a ${25}^{\circ }$ angle, a ${145}^{\circ }$ angle and a ${265}^{\circ }$ angle.

Answer to Problem 64E

  $\text{For }\theta ={25}^{\circ },{25}^{\circ }+{360}^{\circ }k,\text{ where }k\text{ is any integer except 0}$

  $\text{For }\theta ={145}^{\circ },{145}^{\circ }+{360}^{\circ }k,\text{ where }k\text{ is any integer except 0}$

  $\text{For }\theta ={265}^{\circ },{265}^{\circ }+{360}^{\circ }k,\text{ where }k\text{ is any integer except 0}$

Explanation of Solution

Given information: Critical Thinking: A ${25}^{\circ }$ angle, a ${145}^{\circ }$ angle and a ${265}^{\circ }$ angle

Calculation:

For any angle $\theta ,$ the coterminal angles with it are always multiples of ${360}^{\circ }$ add or subtracted from the original angle or….

Coterminal angles of $\theta$ are found at ${360}^{\circ }k$ rotational intervals where k is an integer.

  $\text{For }\theta ={25}^{\circ },{25}^{\circ }+{360}^{\circ }k,\text{ where }k\text{ is any integer except 0}$ (0 would give you the original angle)

  $\text{For }\theta ={145}^{\circ },{145}^{\circ }+{360}^{\circ }k,\text{ where }k\text{ is any integer except 0}$ (0 would give you the original angle)

  $\text{For }\theta ={265}^{\circ },{265}^{\circ }+{360}^{\circ }k,\text{ where }k\text{ is any integer except 0}$ (0 would give you the original angle)