calculate csc(30°)

⚠ Degrees → radians: multiply by $\frac{\pi }{180}$, so the expression becomes $\csc (\frac{30}{180}·\pi )$

The cosecant is read as $\csc \left(u\right)=\frac{1}{\sin \left(u\right)}$, on each interval where $\sin \left(u\right)\ne 0$

Let's calculate: $\frac{1}{\sin (\frac{30}{180}\times \pi )}$

We simplify the fraction: $\frac{30}{180}$ by the common factor: $30$ to get the new fraction: $\frac{1}{6}$

$\frac{1}{\sin (\frac{1}{6}\times \pi )}$

ⓘ The sine is the y-coordinate (vertical axis) of the point reached on the unit circle after a rotation of $\frac{1}{6}\times \pi$ radians from the horizontal axis pointing to the right, this is a remarkable value: $\sin (\frac{1}{6}\times \pi )$ = $\frac{1}{2}$

$\frac{1}{\frac{1}{2}}$

ⓘ Dividing is multiplying by the reciprocal: $\frac{1}{\frac{1}{2}}$ = $2$

▶Result:   $2$