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$\tan(\theta) = -\frac{15}{8}$ given that $\theta$ is in quadrant II

I know that $x= -8$ and $y= 15$ since it is in quadrant II $x$ has to be the negative. Where do I go from here? I tried $\tan^2\theta - \sec^2\theta = 1$ got some nonsensical answers.

Not sure how the $-\frac{15}{8}$ functions either, bad math on my part I know but I don't know if it squared is positive or negative. I mean logically to me it is positive but I am not sure, I can't get a proper answer either way.

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Sorry, I don't see a question here. Adam, what do you actually want? – Gerry Myerson Jun 2 '11 at 0:25
It would really help us to help you if you could specifically ask what it is you need to do: find the angle? find trig values for the angle? both? As @Gerry has said above, what is your question? – amWhy Jun 2 '11 at 0:32
Sorry the question was in the title, I need to find the trig function values. – Adam Jun 2 '11 at 0:55
up vote 3 down vote accepted

You can compute $r=\sqrt{x^2+y^2}=\sqrt{(-8)^2+15^2}=17$ and evaluate the trig functions as in this answer by user6312 to a question of yours.

Added: In response to your comment. Edited: For the remaing trigonometric functions you have, by definition, the following five fractions:

  • $\cos\theta=\frac{x}{r}$,
  • $\sin\theta=\frac{y}{r}$,
  • $\cot\theta=\frac{1}{\tan\theta}=\frac{x}{y}$,
  • $\sec\theta=\frac{1}{\cos\theta}=\frac{r}{x}$,
  • $\csc\theta=\frac{1}{\sin\theta}=\frac{r}{y}$.

To find their values you just have to substitute $x=-8$, $y=15$ (found by you) and $r=17$ (evaluated above) in these expressions.

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My problem is I am not sure how to do that. – Adam Jun 2 '11 at 0:56
@Adam: I added and edited my answer. – Américo Tavares Jun 2 '11 at 15:11

Draw a picture! You can then get all six triggies easily.

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To expand: plot that point $x=-8$, $y=15$. Draw the line segment from it to the origin, and the vertical line segment connecting it to the $x$-axis. See the triangle? How long is the horizontal side? How long is the vertical side? At what angle do those two sides meet? What is the length of the other side? How do you express the trig functions in terms of the sides of the triangle? – Gerry Myerson Jun 2 '11 at 1:09
I have no idea how to look at a graph and get a length, I mean if it is straight I can count dashes on the graph but that is it. What is it isn't straight? – Adam Jun 2 '11 at 1:53
@Adam, did you see the question, "At what angle do those two sides meet?" Do you know what people call that kind of triangle? Do you know anything about the lengths of the sides of that kind of triangle? – Gerry Myerson Jun 2 '11 at 3:38

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