Expert: Steve Holleran - 9/14/2007

Question
Find the sin of an angle if the terminal side of the angle lies along the line y=-3x in quadrant II.

My answer was -1/3.  My book says the answer is -3.  Can you explain why my answer is wrong?

Answer
Hi Remona,

I'm a little confused.  The subject of your question says "finding tan" but the question is about the sin.   I'm not sure which one you want, but we can find both.

If the terminal side in Q II is along y = -3x, taking x = -1, we get y = 3.  So, drawing a reference triangle from (-1,3) to the x-axis, the opposite side to the reference angle is 3, the adjacent side is -1 and the hypotenuse is sqrt(10).

So, the sine = opp/hyp = 3/sqrt(10)

   the tan  = opp / adj = 3/-1 = -3

I hope one of these is what you wanted.

Steve Holleran