# How do you find the exact values of six trigonometric functions of t given (sqrt 3/2, 1/2)?

$\sin \left(t\right) = \frac{1}{2}$;$\textcolor{w h i t e}{\text{XXXX}}$$\cos \left(t\right) = \frac{\sqrt{3}}{2}$;$\textcolor{w h i t e}{\text{XXXX}}$$\tan \left(t\right) = \frac{1}{\sqrt{3}}$
$\csc \left(t\right) = 2$;$\textcolor{w h i t e}{\text{XXXX}}$$\sec \left(t\right) = \frac{2}{\sqrt{3}}$;$\textcolor{w h i t e}{\text{XXXX}}$$\cot \left(t\right) = \sqrt{3}$
Assuming the point given is the terminal point of an angle, $t$, in standard Cartesian coordinate position,
the angle is ${30}^{o}$ and the six trigonometric values can be read directly from the image below, base on the definition of those functions.