@e.mccormick which angle is theta?

Question

studygurl14 · Answer

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e.mccormick · Answer

Theta is, by definition of the unit circle, from the (0,1) coordinate swung over to the point.  However, you can use the reference angle inside the circle to find the values if you want nd then the +- rules for quad 2 to make sure you have the correct answer.

studygurl14 · Answer

I'm confused...

e.mccormick · Answer

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e.mccormick · Answer

Reference angles are always < 90.

studygurl14 · Answer

oh...so how do i find sec theta if it isn't even in the triangle?

e.mccormick · Answer

However, you can use the x,y coordinate definitions.

For a radius of r:
$\sin=\dfrac{y}{r}$

$\cos=\dfrac{x}{r}$

If it was a unit circle, r would be 1.  But this is some line, so you need to find r first.  r for radius, which is also h for hypotenuse.  So, distance formula!

studygurl14 · Answer

i think i found the answer...4.123

e.mccormick · Answer

Or adapt thr Pythagorean Formula for Hypotenuse... same thing....

Hmm...  I did not do the math.

$(-1)^2+4^2=17$

$\sqrt{17}\approx 4.123$

So that is r or the hypotenuse.

e.mccormick · Answer

The secent is the inverse of cos, so $\dfrac{r}{x}$ and since x is -1, your answer is off a bit.

e.mccormick · Answer

$\dfrac{\sqrt{17}}{-1}$  Do you see the problem with your answer?

e.mccormick · Answer

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studygurl14 · Answer

thanks. i do see. :)