Find the tangent of an angle $ heta$ on the unit circle in different quadrants
Answer 1
Samuel Scott
To find the tangent of an angle $\theta$ on the unit circle, note that $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$. Consider the following angles:
1. For $\theta = \frac{\pi}{4}$ in the first quadrant:
$\tan\left(\frac{\pi}{4}\right) = \frac{\sin\left(\frac{\pi}{4}\right)}{\cos\left(\frac{\pi}{4}\right)} = 1$
2. For $\theta = \frac{3\pi}{4}$ in the second quadrant:
$\tan\left(\frac{3\pi}{4}\right) = \frac{\sin\left(\frac{3\pi}{4}\right)}{\cos\left(\frac{3\pi}{4}\right)} = -1$
3. For $\theta = \frac{5\pi}{4}$ in the third quadrant:
$\tan\left(\frac{5\pi}{4}\right) = \frac{\sin\left(\frac{5\pi}{4}\right)}{\cos\left(\frac{5\pi}{4}\right)} = 1$
4. For $\theta = \frac{7\pi}{4}$ in the fourth quadrant:
$\tan\left(\frac{7\pi}{4}\right) = \frac{\sin\left(\frac{7\pi}{4}\right)}{\cos\left(\frac{7\pi}{4}\right)} = -1$
Answer 2
Daniel Carter
To find the tangent of an angle $ heta$ on the unit circle, use $ an( heta) = frac{sin( heta)}{cos( heta)}$. Consider the following:
1. For $ heta = frac{pi}{4}$, $ anleft(frac{pi}{4}
ight) = 1$
2. For $ heta = frac{3pi}{4}$, $ anleft(frac{3pi}{4}
ight) = -1$
3. For $ heta = frac{5pi}{4}$, $ anleft{frac{5pi}{4}
ight) = 1$
4. For $ heta = frac{7pi}{4}$, $ anleft(frac{7pi}{4}
ight) = -1$
Answer 3
James Taylor
To find $ an( heta)$ on the unit circle:
1. $ anleft(frac{pi}{4}
ight) = 1$
2. $ anleft(frac{3pi}{4}
ight) = -1$
3. $ anleft(frac{5pi}{4}
ight) = 1$
4. $ anleft(frac{7pi}{4}
ight) = -1$
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