The terminal side of #theta# in standard position contains (-6,8), how do you find the exact values of the six trigonometric functions of #theta#?

1 Answer
Feb 28, 2018

Answer:

See explanation.

Explanation:

If the point in the angle's terminal side is #P=(x,y)# then the trigonometric functions can be calculated as:

#sin alpha=y/r#

#cos alpha=x/r#

#tan alpha=y/x#

#cot alpha=x/y#

#sec alpha=r/x#

#csc alpha=r/y#

where #r=sqrt(x^2+y^2)#

For the given point we have:

#r=sqrt((-6)^2+8^2)=sqrt(36+64)=10#

So the functions are:

#sin alpha=8/10=4/5#

#cos alpha=(-6)/10=-3/5#

#tan alpha=8/(-6)=-4/3#

#cot alpha=(-6)/8=-3/4#

#sec alpha=10/(-6)=-5/3=-1 2/3#

#csc alpha=10/8=5/4=1 1/4#