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

1 Answer
Apr 27, 2017

See explanation.

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#