How do you find the exact value of the six trigonometric functions of the angle whose terminal side passes through #(3,-4)#?

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Answer 1 · 2017-04-27T16:26:56

See explanation.

To find the values of all the trigonometric functions first you have to find the distance between the point on the angle's side and the origin.

Here the distance is:

#r=sqrt((3-0)^2+(-4-0)^2)=sqrt(3^3+4^2)=sqrt(25)=5#

Now we can calculate the functions:

#sin alpha=y/r=(-4)/5=-0.8#

#cos alpha=x/r=3/5=0.6#

#tan alpha=y/x=(-4)/3=-1 1/3#

#cot alpha = x/y=3/-4=-3/4#

#sec alpha=r/x=5/3=1 2/3#

#csc alpha = r/y=5/-4=-5/4=-1 1/4#