anonymous
  • anonymous
Find the point on the terminal side of θ = -3pie/4 that has an x coordinate of -1. Show full work.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Yttrium
  • Yttrium
Maybe it's time for you to do this work. :)) Just show me what you can. I'll support you.
DebbieG
  • DebbieG
Remember that for ANY point on the terminal side of \(-3\pi/4\), \[\large \tan \left(-\dfrac{3\pi}{4}\right)=\frac{ y }{ x }\] So if you know that tangent value (you should, it's a standard unit circle angle), then just set that = to y/(-1) and find the y coordinate.
anonymous
  • anonymous
Should my answer me a fraction or a decimal?

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anonymous
  • anonymous
Be*
anonymous
  • anonymous
is it y = 13.42?
anonymous
  • anonymous
@DebbieG ?
anonymous
  • anonymous
@PFEH.1999 can you maybe help me with this?
anonymous
  • anonymous
Wow really? Thanks everyone!
DebbieG
  • DebbieG
No, that's not the y value. Can you show how you got that?
anonymous
  • anonymous
Its not? I set it = to y/ -1 and cross multiplied
DebbieG
  • DebbieG
you set WHAT = y/(-1)? \(\large \tan \left(-\dfrac{3\pi}{4}\right)=\frac{ y }{ x }\) Should be the TANGENT VALUE that you are setting = y/(-1). What is \(\large \tan \left(-\dfrac{3\pi}{4}\right)\)?
anonymous
  • anonymous
Im not sure how to find the Tangent value of that
DebbieG
  • DebbieG
ok, well, that's a critical part here. You are doing function values with unit circle angles, so how have you been taught to do them? Have you learned the two "special" right triangles and the side ratios? |dw:1378898204001:dw|
DebbieG
  • DebbieG
Or, are you supposed to refer to a unit circle?
DebbieG
  • DebbieG
Since you are given this problem, it's clear that you are - somehow - supposed to know (or be able to find) the tangent value.
DebbieG
  • DebbieG
Another approach to finding y, if you understand the triangle approach would be this: |dw:1378898438029:dw|
anonymous
  • anonymous
I was taught to use Soh Cah Toa
anonymous
  • anonymous
But what i dont understand is what is the opposite/adjacent of tan in this particular problem?
DebbieG
  • DebbieG
Well, the 45-45-90 triangle is symmetric with respect to the two 45* angles, so it doesn't matter which one you use. The opposite and adjacent "result" will be the same. Or, if you are using the sketch in the coordinate plane:|dw:1378898882284:dw|
anonymous
  • anonymous
Im sorry im not understanding this, but then what would the tangent value of -3pie/4?
Yttrium
  • Yttrium
@MandyNeedsHelp , you can use the reference angle 45 degrees to solve for the tangent value of -3pi/4. But always take a look at the signs of your x and y because it is found on the 3rd quadrant. :)
Yttrium
  • Yttrium
Did you understand what I tell you?
anonymous
  • anonymous
I know but how do i use the reference angle 45 to solve it ?
Yttrium
  • Yttrium
Do you know what tan45 equal to?
anonymous
  • anonymous
1 right?
Yttrium
  • Yttrium
how do you arive at 1?
anonymous
  • anonymous
I dont know i put it in the calculator
Yttrium
  • Yttrium
Let me tell you this one, tan is also equal to sine/cosine sine 45 = what? cos 45 = what? Then how do you arrive at tan45=1? Can you show me now?
anonymous
  • anonymous
sin 45 = 0.707106781186547 cos 45 = 0.707106781186548 0.707106781186547/0.707106781186548 =1
Yttrium
  • Yttrium
Can you do it without decimal? I mean, using radicals?
anonymous
  • anonymous
Im just trying to find the answer to this question so i can try to do some on my own, can you please explain to me how i can ge the answer.
Yttrium
  • Yttrium
actually, sine45 = sqrt2/2 and cos45 = sqrt2/2 using the tangent fuction, you'll get tan = sin/cos or y/x therefore, tan45 = (sqrt2/2)/(sqrt2/2) therefore, your y = sqrt2/2 and your x = sqrt2/2 knowing the fact that -3pi/4 is found on the 3rd quadrant hence your x and y must be negative so, y = -sqrt2/2 and x = -sqrt2/2
anonymous
  • anonymous
I understand it when its laid out for me like that, but is tat the final answer?
Yttrium
  • Yttrium
Yes. Since we're talking about points, therefore the answer should be in a coordinate x and y. :)
anonymous
  • anonymous
But the question was asking for the point on the terminal side that has an x coordinate of -1?
Yttrium
  • Yttrium
oh sorry, I didn't see that |dw:1378955764913:dw| with that you can use tan45 = opp/adj (y is the opp and -1 is the adjacent) Substite tan45 1 = y/-1 Therefore, y = -1 Hence, the point is (-1,-1)
anonymous
  • anonymous
Now that i can understand! Thank you so much for everything i appreciate it.
Yttrium
  • Yttrium
No problem. :)
DebbieG
  • DebbieG
@MandyNeedsHelp , you asked "I know but how do i use the reference angle 45 to solve it ?" This is what I was getting at earlier... if you know the "special triangles" (you should memorize them if you don't, they will come in handy!!), then just use the 45-45-90 triangle: |dw:1378902327565:dw|
DebbieG
  • DebbieG
You'll have a much easier time in trig if you get comfortable with computing the function values this way for all the multiples of 30*, 45* and 60* (and know how to go back and for between degrees and radians for these angles). I tell my trig students that knowing how to "cook up" THESE function values it to your trig class, what the multiplication tables are to a 3rd grade math class - they are that fundamental and that important to understand. :) It just takes a bit of practice to get the hang of it!
DebbieG
  • DebbieG
Here are two handouts that I developed, you might find them helpful.
anonymous
  • anonymous
Thank you so much, this is great information, ill make sure to look through it

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