SOLUTION: Dear Sir/Madam, I am confronted with the following problem: "The point (12,-16) is on the terminal side of the angle theta. Find tan(theta)." I am a little confused as to

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Dear Sir/Madam, I am confronted with the following problem: "The point (12,-16) is on the terminal side of the angle theta. Find tan(theta)." I am a little confused as to       Log On

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Question 6510: Dear Sir/Madam,
I am confronted with the following problem:
"The point (12,-16) is on the terminal side of the angle theta. Find tan(theta)."
I am a little confused as to what they mean by terminal side. I played around with this question and got the answer to be -4/3, which is right, but could you explain the terminal side idea to me a bit?
Thanks in advance.
Regards,
-Mike
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
i have never come across this terminolgy before - i guess it is an Americanism.
Anyway, looking on the web, it is as follows:

Start with the x-axis as the "initial side". Then turn to point at the coordinate (here, (12,-16)). The line you end up on (the hypotenuse in this case) is the terminal side.

So, sketching axes. Plot the point (12, -16) in the 4th quadrant. Start at the origin, pointing along the +ve x-direction and then turn to the point to create the hypotenuse..this is your angle +theta+, and then tan%28theta%29 = opp/adj which gives

tantheta = -16/12
tantheta = -4/3

jon.