If #sectheta=-4/3# is negative and #cottheta# is positive, find all the trigonometric ratios?

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Answer 1 · 2017-06-19T07:06:16

#sintheta=-sqrt7/4#, #costheta=-3/4#
#tantheta=sqrt7/3#, #cottheta=3/sqrt7#
#sectheta=-4/3# and #csctheta=-4/sqrt7#

As #sectheta# is negative and #cottheta# is positive, #theta# lies in #Q3# and

while #tan# and #cot# ratios are positive, all other ratios are negative.

As #sectheta=-4/3#, #costheta=-3/4#

#tantheta=sqrt((-4/3)^2-1)=sqrt(16/9-1)=sqrt7/3#

#cottheta=3/sqrt7#

#sintheta=tanthetaxxcostheta=sqrt7/3xx(-3)/4=-sqrt7/4#

and #csctheta=-4/sqrt7#