The terminal side of #theta# in standard position contains (4,-2), how do you find the exact values of the six trigonometric functions of #theta#?

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Answer 1 · 2018-02-03T17:47:13

See explanation.

The point's coordinates are:

#x=4#, #y=-2#

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

#r=sqrt(x^2+y^2)=sqrt(4^2+(-2)^2)=sqrt(16+4)=sqrt(20)=2sqrt(5)#

Now we can calculate the functions:

#sintheta=y/r=-2/(2sqrt(5))=-sqrt(5)/5#

#costheta=x/r=4/(2sqrt(5))=2/sqrt(5)=(2sqrt(5))/5#

#tantheta=y/x=-2/4=-1/2#

#cottheta=x/y=4/-2=-2#

#sectheta=r/x=(2sqrt(5))/4=sqrt(5)/2#

#csctheta=r/y=(2sqrt(5))/-2=-sqrt(5)#