How do you use fundamental identities to find the values of the trigonometric values given sin X = - 5/13 and tan X > 0?

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Answer 1 · 2017-02-08T17:08:54

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

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

As #sinx=-5/13# and #tanx>0# i.e. positive,

#cosx# which is #sinx/tanx# is negative.

Hence #cosx=-sqrt(1-sin^2x)=-sqrt(1-(-5/13)^2)#

= #-sqrt(1-25/169)=-sqrt(144/169)=-12/13#

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

#cotx=1/tanx=12/5#

#secx=1/cosx=-13/12# and

#cscx=1/sinx=-13/5#