How do you find the values of the six trigonometric functions given #tantheta=-15/8# and #sintheta<0#?

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Answer 1 · 2017-01-15T06:40:23

#sintheta=-15/17#, #costheta=8/17#, #tantheta=-15/8#
#cottheta=-8/15#, #sectheta=17/8#, #csctheta=-17/15#

As #tantheta=-15/8# and #sintheta<0# i.e. both are negative,

#theta# is in Q4 - fourth quadrant and while #costheta# and #sectheta# are positive, rest of the four trigonometric functions are negative.

Now as #tantheta=-15/8#, #cottheta=-8/15# and

#sectheta=sqrt(1+tan^2theta)=sqrt(1+225/64)=sqrt289/64=17/8#

#:.costheta=1/sectheta=8/17#

#sintheta=tanthetaxxcostheta=-15/8xx8/17=-15/17#

and #csctheta=-17/15#