Given #sin^2 theta+cos^2theta=1#, #sin theta = ##(8sqrt185)/(185)#, and #pi/2<=theta<=(3pi)/2#, what is the value of #tan theta#?

1 Answer
Monzur R.
May 21, 2017

#tantheta=-8/11#

Explanation:

#sintheta=(8sqrt185)/185=8/sqrt185#

We are told that #pi/2 <= theta <= (3pi)/2#. This means that #costheta <= 0#. Also, since #sintheta > 0#, #tantheta < 0#.

#costheta=-sqrt(1-sin^2theta)=-11/sqrt185#

#tantheta=sintheta/costheta=(8/sqrt185)/(-11/sqrt185)=-8/11#

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