How do you find #sintheta# and #tantheta# if the terminal side of #theta# lies along the line #y=-3x# in QIV?

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Answer 1 · 2018-03-01T07:49:53

See exdplanation.

#QIV# is the quadrant where #x>0# and #y<0#, so the example point can be #(1,-3)#

To calculate the 6 functions we have to calculate the distance between the point and the origin:

#r=sqrt(1^2+(-3)^2)=sqrt(1+9)=sqrt(10)#

Now we can calculate the functions:

#sin alpha=y/r=(-3)/sqrt(10)=-(3sqrt(10))/10#

#cos alpha=x/r=1/sqrt(10)=sqrt(10)/10#

#tan alpha=y/x=-3/1=-3#

#cot alpha=x/y=1/(-3)=-1/3#

#sec alpha=r/x=sqrt(10)#

#csc alpha=r/y=sqrt(10)/(-3)=-sqrt(10)/3#