ringearV

2021-08-14

Find 6 - trigonometry function value of $\theta =\frac{3\pi }{2}$

### Answer & Explanation

Calculation:
Compute the trigonometric function values of $\frac{3\pi }{2}$ as follows.
$\mathrm{sin}\left(\frac{3\pi }{2}\right)=\mathrm{sin}\left(2\pi -\frac{\pi }{2}\right)=-1$
$\mathrm{csc}\left(\frac{3\pi }{2}\right)=\frac{1}{\mathrm{sin}\left(\frac{3\pi }{2}\right)}=-1$
$\mathrm{cos}\left(\frac{3\pi }{2}\right)=\mathrm{cos}\left(2\pi -\frac{\pi }{2}\right)=0$
Similarly, other trigonometric function values are
$\mathrm{sec}\left(\frac{3\pi }{2}\right)=\frac{1}{\mathrm{cos}\left(\frac{3\pi }{2}\right)}=\text{undefined}$
$\mathrm{tan}\left(\frac{3\pi }{2}\right)=\frac{\mathrm{sin}\left(\frac{3\pi }{2}\right)}{\mathrm{cos}\left(\frac{3\pi }{2}\right)}=\text{undefined}$
$\mathrm{cot}\left(\frac{3\pi }{2}\right)=\frac{\mathrm{cos}\left(\frac{3\pi }{2}\right)}{\mathrm{sin}\left(\frac{3\pi }{2}\right)}=0$
The 6 trigonometric function values of $\theta =\frac{3\pi }{2}$ are as follows.
$\mathrm{sin}\left(\frac{3\pi }{2}\right)=-1$
$\mathrm{cos}\left(\frac{3\pi }{2}\right)=0$
$\mathrm{csc}\left(\frac{3\pi }{2}\right)=-1$
$\mathrm{sec}\left(\frac{3\pi }{2}\right)=\text{undefined}$
$\mathrm{tan}\left(\frac{3\pi }{2}\right)=\text{undefined}$
$\mathrm{cot}\left(\frac{3\pi }{2}\right)=0$

Jeffrey Jordon