How do you find the values of the six trigonometric functions given #costheta=8/17# and #tantheta<0#?

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Answer 1 · 2017-01-07T07:37:15

#costheta=8/17#

#sintheta=-15/17#

#tantheta=-15/8#

#cottheta=-8/15#

#sectheta=17/8#

#csctheta=-17/15#

Since

#costheta>0#

and

#tantheta<0#,

the angle is in the fourth quadrant, where

#sintheta<0#,

then
#sintheta=-sqrt(1-cos^2theta)=-sqrt(1-(8/17)^2)=-sqrt(1-64/289)=-sqrt(225/289)=-15/17#

#tantheta=sintheta/costheta=(-15/cancel17)/(8/cancel17)=-15/8#

#cottheta=1/tantheta=-8/15#

#sectheta=1/costheta=17/8#

#csctheta=1/sintheta=-17/15#