Find the $csc( heta)$ of an angle in the unit circle

Answer 1

To find the $\csc(\theta)$ of an angle $\theta$ in the unit circle, first determine the sine of the angle. The cosecant is the reciprocal of the sine.

For example, consider $\theta = \frac{\pi}{6}$.

$\sin(\frac{\pi}{6}) = \frac{1}{2}$

Therefore,

$\csc(\frac{\pi}{6}) = \frac{1}{\sin(\frac{\pi}{6})} = \frac{1}{\frac{1}{2}} = 2$

Answer 2

To find $csc( heta)$ on the unit circle, you need to take the reciprocal of $sin( heta)$.

For example, if $ heta = frac{pi}{4}$:

$sin(frac{pi}{4}) = frac{sqrt{2}}{2}$

Thus,

$csc(frac{pi}{4}) = frac{1}{sin(frac{pi}{4})} = frac{1}{frac{sqrt{2}}{2}} = sqrt{2}$

Answer 3

To find $csc$ in the unit circle:

For $ heta = frac{pi}{3}$:

$sin(frac{pi}{3}) = frac{sqrt{3}}{2}$

So,

$csc(frac{pi}{3}) = frac{2}{sqrt{3}} = frac{2sqrt{3}}{3}$

Start Using PopAi Today