Find the $ an$ values of the unit circle at specific angles
Answer 1
Emily Hall
To find the $\tan$ values of the unit circle at specific angles, we can use the fact that $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$:
1. At $\theta = \frac{\pi}{4}$, $ \tan(\frac{\pi}{4}) = \frac{\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{4})} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $
2. At $\theta = \frac{3\pi}{4}$, $ \tan(\frac{3\pi}{4}) = \frac{\sin(\frac{3\pi}{4})}{\cos(\frac{3\pi}{4})} = \frac{\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} = -1 $
3. At $\theta = \pi$, $ \tan(\pi) = \frac{\sin(\pi)}{\cos(\pi)} = \frac{0}{-1} = 0 $
Answer 2
Thomas Walker
To determine the $ an$ values on the unit circle at key radians, utilize $ an( heta) = frac{sin( heta)}{cos( heta)}$:
1. For $ heta = frac{pi}{6}$: $ an(frac{pi}{6}) = frac{sin(frac{pi}{6})}{cos(frac{pi}{6})} = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} $
2. For $ heta = frac{2pi}{3}$: $ an(frac{2pi}{3}) = frac{sin(frac{2pi}{3})}{cos(frac{2pi}{3})} = frac{frac{sqrt{3}}{2}}{-frac{1}{2}} = -sqrt{3} $
3. For $ heta = frac{5pi}{6}$: $ an(frac{5pi}{6}) = frac{sin(frac{5pi}{6})}{cos(frac{5pi}{6})} = frac{frac{1}{2}}{-frac{sqrt{3}}{2}} = -frac{1}{sqrt{3}} $
Answer 3
Samuel Scott
Calculate the $ an$ values at the following angles:
1. $ heta = frac{pi}{3}$: $ an(frac{pi}{3}) = frac{sin(frac{pi}{3})}{cos(frac{pi}{3})} = sqrt{3} $
2. $ heta = frac{pi}{2}$: $ an(frac{pi}{2}) = frac{sin(frac{pi}{2})}{cos(frac{pi}{2})} = ext{undefined} $
3. $ heta = frac{7pi}{4}$: $ an(frac{7pi}{4}) = frac{sin(frac{7
Start Using PopAi Today