How do you determine all trigonometric ratios given secθ=6/5?

1 Answer
Nov 17, 2015

sintheta=sqrt11/6,tantheta=sqrt11/5,costheta=5/6,
csctheta=(6sqrt11)/11, cottheta=(5sqrt11)/11

Explanation:

If sectheta = 6/5
costheta=1/(sectheta)=5/6

sin^2theta+cos^2theta=1
sintheta=sqrt(1-cos^2theta)=sqrt(1-(5/6)^2)=sqrt11/6

csctheta=1/sintheta=6/sqrt11=(6sqrt11)/11

1+tan^2theta=sec^2theta
tantheta=sqrt(sec^2theta-1)=sqrt((6/5)^2-1)=sqrt11/5

cottheta=1/tantheta=5/sqrt11=(5sqrt11)/11