How do you find the remaining trigonometric functions of #theta# given #sin theta=12/13# and #theta# terminates in QI?

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Answer 1 · 2017-03-01T08:58:10

#sinx=12/13#, #cosx=5/13#, #tanx=12/5#

#cotx=5/12#, #secx=13/5# and #cscx=13/12#

As #theta# terminates in #QI#, all trigonometric ratios are positive.

#:.cosx=sqrt(1-sin^2x)=sqrt(1-(12/13)^2)#

= #sqrt(1-144/169)=sqrt(25/169)=5/13#

and #tanx=sinx/cosx=(12/13)/(5/13)=12/13xx13/5=12/5#

and #cotx=1/tanx=5/12#, #secx=1/cosx=13/5# and

#cscx=1/sinx=13/12#