# terminal side

• Oct 3rd 2012, 10:57 AM
RiderMind
Hello. I am having difficulty with this problem:
Find the point on the terminal side of θ = ​-3pi/4 that has an x coordinate of -1

I was hoping that someone here would be able to help me out? I am actually trying to figure out what I am doing so if you could explain how you found the answer, I would really appreciate it. Thank you so much guys.
• Oct 3rd 2012, 11:01 AM
MarkFL
Re: terminal side
θ = ?
• Oct 3rd 2012, 11:02 AM
RiderMind
Re: terminal side
oops, sorry.

θ=-3pi/4

Thanks
• Oct 3rd 2012, 11:10 AM
MarkFL
Re: terminal side
From the given information, we know:

$\displaystyle r\cos\left(-\frac{3\pi}{4} \right)=-1$

$\displaystyle r=\sqrt{2}$

The $\displaystyle y$-coordinate is then:

$\displaystyle r\sin\left(-\frac{3\pi}{4} \right)=?$
• Oct 3rd 2012, 11:58 AM
RiderMind
Re: terminal side
0?
• Oct 3rd 2012, 12:15 PM
MarkFL
Re: terminal side
No, what is $\displaystyle \sin\left(-\frac{3\pi}{4} \right)=-\sin\left(\frac{3\pi}{4} \right)=-\sin\left(\pi-\frac{3\pi}{4} \right)=-\sin\left(\frac{\pi}{4} \right)$ ?
• Oct 3rd 2012, 12:30 PM
RiderMind
Re: terminal side
-45 degrees?

or sqrt2
• Oct 3rd 2012, 12:37 PM
MarkFL
Re: terminal side
No, the sine of an angle will not return an angle. $\displaystyle \frac{\pi}{4}$ is a special angle for which you should know the trig. functions at that angle.

$\displaystyle -\sin\left(\frac{\pi}{4} \right)=-\frac{1}{\sqrt{2}}$

So, the $\displaystyle y$-coordinate of the point is:

$\displaystyle y=r\cdot\left(-\frac{1}{\sqrt{2}} \right)$

Recall we found $\displaystyle r=\sqrt{2}$ hence:

$\displaystyle y=\sqrt{2}\cdot\left(-\frac{1}{\sqrt{2}} \right)=-1$

And so, the point in question is (-1,-1). Try drawing a diagram, and you will easily see that the $\displaystyle y$-coordinate has to be equal to the $\displaystyle x$-coordinate, as the given angle lies along the line $\displaystyle y=x$.
• Oct 3rd 2012, 12:52 PM
RiderMind
Re: terminal side
I see what you mean now. Thanks for telling me to draw a diagram. That made it easier for me to understand. So -pi/4 is one of those I just need to memorize then right?

Thanks so much bro.
• Oct 3rd 2012, 01:06 PM
HallsofIvy
Re: terminal side
Well, it's a lot easier to memorize if you understand it. Imagine a right triangle having one angle of $\displaystyle \pi/4$ and one leg of length 1. Since $\displaystyle \pi/2= 2(\pi/4)$, so that the other angle is also $\displaystyle \pi/4$ which means that the other leg also has length 1. By the Pythagorean theorem, the length of the hypotenuse is given by $\displaystyle c^2= 1^2+ 1^2= 2$ so that $\displaystyle c= \sqrt{2}$. That gives $\displaystyle sin(\pi/4)= 1/\sqrt{2}= \frac{\sqrt{2}}{2}$.
• Oct 3rd 2012, 06:02 PM
Nervous
Re: terminal side
Could someone send me a link to teach me how to do this? I'm afraid I don't even understand it...