Question

What are the six trig function values of `pi/36`?

Answer 1

As far as I know there is no exact algebraic expression, so we are stuck with approximations...

Explanation:

`sin(pi/36) ~~ 0.08715574275`

`cos(pi/36) ~~ 0.99619469809`

`tan(pi/36) ~~ 0.08748866353`

`csc(pi/36) ~~ 11.47371324567`

`sec(pi/36) ~~ 1.00381983754`

`cot(pi/36) ~~ 11.43005230276`

They are related algebraically as follows:

Let `alpha = sin(pi/36)`

Then:

`sin(pi/36) = alpha`

`cos(pi/36) = sqrt(1-alpha^2)`

`tan(pi/36) = alpha/sqrt(1-alpha^2)`

`csc(pi/36) = 1/alpha`

`sec(pi/36) = 1/sqrt(1-alpha^2)`

`cot(pi/36) = sqrt(1-alpha^2)/alpha`