katherinesmith
  • katherinesmith
i need serious help with trigonometric values in the four quadrants of a circle.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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katherinesmith
  • katherinesmith
i have read my lesson over again 2 times and still can not figure out the process to solving something like this: what is the exact value of sin \[\frac{ \pi }{ 2}\] as found on the unit circle?
katherinesmith
  • katherinesmith
sin goes in front of the fraction
katherinesmith
  • katherinesmith
any idea @zepdrix ?

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zepdrix
  • zepdrix
Ok let's start really basic first. Do you know your orientation within the unit circle? Like do you know where an angle of \(\large \theta=0\) starts? And do you know which way to rotate and how far to go to get to \(\large \pi/2\) ?
katherinesmith
  • katherinesmith
i know pi/2 is equivalent to 90 degrees
zepdrix
  • zepdrix
ok good.
zepdrix
  • zepdrix
|dw:1377747637549:dw|
zepdrix
  • zepdrix
|dw:1377747711955:dw|Before we figure this problem out ~ I just wanna make 2 really quick notes that I think might help. Let's start with some arbitrary angle like this.
zepdrix
  • zepdrix
|dw:1377747788638:dw|There are a couple ways to get to this point on the unit circle. By spinning theta radians around the circle OR by moving a distance in the x direction, and a distance in the y direction.
zepdrix
  • zepdrix
|dw:1377747862223:dw|Our trig functions show us how x and y relate to the angle. In the unit circle: `x corresponds to cosine of our angle` `y corresponds to sine of our angle`
zepdrix
  • zepdrix
|dw:1377748018329:dw|So when our angle is up here at pi/2....
zepdrix
  • zepdrix
When they ask us `What is the SINE of pi/2?` They're asking, `what is the y-component of your angle`.
zepdrix
  • zepdrix
|dw:1377748102085:dw|
zepdrix
  • zepdrix
So what would that be? :x The y-value of that particular point?
katherinesmith
  • katherinesmith
|dw:1377748216852:dw| oh my god i don't know i kinda just made it a triangle. how do i know where to make it!
katherinesmith
  • katherinesmith
you're so good at explaining honestly i'm just stupid
zepdrix
  • zepdrix
To make a triangle only draw a line `straight down`.|dw:1377748252926:dw| But don't worry about doing the triangle thing right now. That might be a little bit too tricky at this point.
katherinesmith
  • katherinesmith
i understand that but the line is at 90 degrees which is straight up so there's no way to make a triangle
zepdrix
  • zepdrix
Yess good observation! :) We can't make a triangle.
zepdrix
  • zepdrix
The question I'm asking you is a lot more simple than it seems. It's just hard to make the connection. Think for a sec :) What is the `y-coordinate` of the point (0,1)?
katherinesmith
  • katherinesmith
1
zepdrix
  • zepdrix
Yay good good. Noooo you're not stupid! :D You're like one of those special cookies.. we just have to... leave it in the oven a little longer than the others. :x
katherinesmith
  • katherinesmith
HAHAHA that is true.
zepdrix
  • zepdrix
Ok so here is the connection.\[\Large \color{royalblue}{y=\sin \theta}\] And we determined that,\[\Large \color{royalblue}{y}=1, \qquad\text{when }\theta=\frac{\pi}{2}\]
katherinesmith
  • katherinesmith
alright.
zepdrix
  • zepdrix
\[\Large \color{royalblue}{\sin\theta}=1, \qquad\text{when }\theta=\frac{\pi}{2}\]\[\Large \color{royalblue}{\sin\frac{\pi}{2}}=1\]
zepdrix
  • zepdrix
Let's try one more real quick!! D: What does this give us?\[\Large \cos \pi=?\]
katherinesmith
  • katherinesmith
what?!
zepdrix
  • zepdrix
|dw:1377748722656:dw|
zepdrix
  • zepdrix
So pi is a distance of half circle right?
katherinesmith
  • katherinesmith
wait a minute. so the answer is 1?
zepdrix
  • zepdrix
yes sin(pi/2)=1 :3
katherinesmith
  • katherinesmith
okay well i have another one of my own, can i ask you?
zepdrix
  • zepdrix
fine fine fine :3
katherinesmith
  • katherinesmith
What is the exact value of \[\cos \frac{ \pi }{ 6 }\] as found on the unit circle
zepdrix
  • zepdrix
Hmm this one is tough to answer without going into some detail. It really depends how much you want to commit to memory. Trig is hard because you have to remember a ton of stuff. So I always feel like the less you have to memorize, the better. There are some good tricks for memorizing the special angles but I think that might be a bit tough for you at this point. :[ http://mathematica.stackexchange.com/questions/2456/generate-a-unit-circle-trigonometry Check out the unit circle in this link.
zepdrix
  • zepdrix
Remember what I told you earlier. Try to burn it into your brain!! x = cos y = sin
katherinesmith
  • katherinesmith
well i have that chart on a piece of paper sitting in front of me
zepdrix
  • zepdrix
Oh good hehe.
katherinesmith
  • katherinesmith
pi/6 is 30 degrees, now i just dont know what to do
zepdrix
  • zepdrix
So if you go to the angle pi/6, what is your x-coordinate? THAT is the value that corresponds to cosine.
zepdrix
  • zepdrix
Do you have the coordinates all written down? If you don't then you'll want to use that link :o
katherinesmith
  • katherinesmith
are you talking about \[\frac{ \sqrt{3} }{ 2 }, \frac{ 1 }{ }\]
katherinesmith
  • katherinesmith
1/2 ^
zepdrix
  • zepdrix
yes. Those are the coordinates of the point along the unit circle that correspond to our angle. cosine pi/6 is given by the `x coordinate`
katherinesmith
  • katherinesmith
okay.

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