Question

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

Answer 1

`sin(t) = 1/2`;`color(white)("XXXX")` `cos(t)=sqrt(3)/2`;`color(white)("XXXX")` `tan(t)=1/sqrt(3)`
`csc(t)=2`;`color(white)("XXXX")` `sec(t)=2/sqrt(3)`;`color(white)("XXXX")` `cot(t)=sqrt(3)`

Explanation:

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.