Question

What are the exact values of the six trigonometric functions of `(3\pi)/4`?

Answer 1

See explanation.

Explanation:

`sin(3/4pi)=sin(pi-pi/4)=sin (pi/4)=sqrt(2)/2`

`cos(3/4pi)=cos(pi-pi/4)=-cos(pi/4)=-sqrt(2)/2`

`tan(3/4pi)=(sin(3/4pi))/(cos(3/4pi))=-1`

`cot(3/4pi)=1/tan(3/4pi)=-1`

`sec(3/4pi)=1/cos(3/4pi)=1/(-sqrt(2)/2)=-2/sqrt(2)=-sqrt(2)`

`csc(3/4pi)=1/sin(3/4pi)=1/(sqrt(2)/2)=2/sqrt(2)=sqrt(2)`