The correct options are a and d because -7pi/4 and 9pi/4 are the required angles.
Important infromation:
- The given angle is [tex]\dfrac{\pi}{4}[/tex].
Angles:
The angles [tex]\theta\pm 2n\pi [/tex] represent the same point on the unit circle as [tex]\theta[/tex].
It means, [tex]\dfrac{\pi}{4}\pm 2n\pi [/tex] represents the same point on the unit circle as [tex]\dfrac{\pi}{4}[/tex].
The required angles are:
[tex]\left\{...,\dfrac{\pi}{4}-4\pi,\dfrac{\pi}{4}-2\pi, \dfrac{\pi}{4},\dfrac{\pi}{4}+2\pi,\dfrac{\pi}{4}+4\pi,...\right\}[/tex]
[tex]\left\{...,-\dfrac{15\pi}{4},-\dfrac{7\pi}{4}, \dfrac{\pi}{4},\dfrac{9\pi}{4},\dfrac{17\pi}{4},...\right\}[/tex]
Therefore, the correct options are a and d.
Find out more about 'Angles' here:
https://brainly.com/question/23475646
