Chapter 4.3, Problem 1E

Solution

To identify: the one angle that is not co terminal with all the others.

  $450°$

Given information:

The angles:

  $150°,510°,-210°,450°,870°$

Definition Used:

Co-terminal angles:

Two angles in the expanded angle-measurement system, which has the same initial side and the same terminal side, yet have different measures are called co-terminal angles.

Angles are co-terminal whenever they differ by an integer multiple of $360°$ or by an integer multiple of $2\pi$ rad.

Explanation:

To find a co-terminal angle for the given angle:

If the angle is given in degrees, then add or subtract the multiples of $360°$ .

If the angle is given in radians, then add or subtract the multiples of  $2\pi$ .

Now, let $150°$ be the angle and try to find the possible co-terminal angles.

  $510°-360°=150°$

So, $510°$ and $150°$ are co-terminal.

Similarly finding for the rest of angles,

  $-210°+360°=150°$

  $450°-360°=90°$

  $\begin{array}{c}870°-2\left(360°\right)=870°-720°\\ =150°\end{array}$

So, it is clear that all the angles other than the angle $450°$ are co-terminal.