Finding Coterminal Angles within a Range
The question is asking for an angle θ that is coterminal with -468°, where θ is between 0° and 360°.
To find a coterminal angle, you need to add or subtract multiples of 360° from the given angle until you find an angle within the specified range. For a negative angle, you would add multiples of 360°.
Let's find the coterminal angle:
θ = -468° + 360°n
Here, n is the number of times we need to add 360° to reach a positive angle within the desired range.
First, let's find the smallest positive angle by adding 360° once:
θ = -468° + 360° = -108°
This is still negative, so we add 360° again:
θ = -108° + 360° = 252°
Now, θ = 252° is in the range from 0° to 360°, so this is the angle that is coterminal with -468° within the specified range.
