If #sectheta = a# and #sintheta < 0#, find the exact valaues of #sintheta#?

Question

I think the answer is like #-sqrt(a^2-1)#

Thanks in advance!!!

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Answer 1 · 2018-05-25T09:04:26

See below

#sectheta=a# and #sin theta>0#

#sectheta=1/costheta=a#

Squaring both sides

#1/cos^2theta=a^2#

#1/a^2=cos^2theta=1-sin^2theta#

Then, transposing terms

#sin^2theta=1-1/a^2#

#sin theta=+-sqrt(1-1/a^2)=+-sqrt(a^2-1)/a#

However #sintheta <0#, then #sintheta=-sqrt(a^2-1)/a#