How do you find the values of the six trigonometric functions given #csctheta=4# and #cottheta<0#?

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Answer 1 · 2018-02-25T16:07:26

#sintheta=1/4#, #costheta=-sqrt15/4#, #tantheta=-1/sqrt15#
#cottheta=-sqrt15#, #sectheta=-4/sqrt15# and #csctheta=4#.

Let us consider the identity #csc^2theta=1+cot^2theta#

as #csctheta=4#, we have #16=1+cot^2theta# and

#cot^2theta=15# and as #cottheta<0#, #cottheta=-sqrt15#

Therefore #tantheta=-1/sqrt15# and #sintheta=1/4#

As #tantheta=sintheta/costheta, this means

#costheta=sintheta/tantheta=(1/4)/(-1/sqrt15)=-sqrt15/4#

and #sectheta=-4/sqrt15#