anonymous
  • anonymous
FAN AND MEDAL The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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jdoe0001
  • jdoe0001
\(\begin{array}{cccllll} (1&,&-1)\\ x&,&y \end{array}\qquad hypotenuse=r=\sqrt{x^2+y^2}\impliedby \textit{pythagorean theorem} \\ \quad \\ \quad \\ sin(\theta)=\cfrac{y}{r} \qquad % cosine cos(\theta)=\cfrac{x}{r} \qquad % tangent tan(\theta)=\cfrac{y}{x}\impliedby \textit{find "r", and plug and chug}\)
anonymous
  • anonymous
Mg I know you from my school :/
anonymous
  • anonymous
@carsonce I'm kinda homeschooled so...

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DanJS
  • DanJS
Draw the thing first
DanJS
  • DanJS
'standard' - relative to the +x axis i believe
DanJS
  • DanJS
|dw:1443138414973:dw|
DanJS
  • DanJS
4th quadrant
DanJS
  • DanJS
You see how the components of that line are at right angles to the x and y axis?
DanJS
  • DanJS
|dw:1443138594122:dw|
anonymous
  • anonymous
yeah
DanJS
  • DanJS
you have right triangles with side lengths of 1
DanJS
  • DanJS
|dw:1443138683435:dw|
DanJS
  • DanJS
you have the side lengths of the right triangle, apply the definition of sin cos and tan to that angle theta, and remember you are in the 4th quadrant
DanJS
  • DanJS
Example \[\sin(\theta) = \frac{ 1 }{ \sqrt{2} }\] \[\theta =\sin^{-1} [\frac{ 1 }{ \sqrt{2} }] = 45\]
DanJS
  • DanJS
So the angle theta is 45, but recall you are in the 4th quadrant
anonymous
  • anonymous
oooooh okay I see now
DanJS
  • DanJS
So the theta is actually from +x CounterClockWise to that terminal side`
DanJS
  • DanJS
360-45 = 315
anonymous
  • anonymous
Thank you for your assistance. I'm usually pretty good at math, but trig is tripping me up so much...
DanJS
  • DanJS
The sin value of theta and (360-theta) are the same, (the y value on the unit circle point)
DanJS
  • DanJS
Right, me too when i took it, realize that the sin function is just the y-coord of the intersection of a line at angle theta through the origin and the unit circle of radius 1
DanJS
  • DanJS
each point ON the unit circle of radius 1 centered at the origin, is (x , y) = ( cos(angle), sin(angle) )
DanJS
  • DanJS
i fyou are that far yet
anonymous
  • anonymous
Ah okay
DanJS
  • DanJS
These may help, solved probs and stuff https://drive.google.com/folderview?id=0B1YZD9uzvB5TfnkzNzg5LU54VC1zUENBNHZoWlUxYXk1OXQtNklXdVVtZnA1T3c4X3hMMWM&usp=drive_web#list
DanJS
  • DanJS
the last 5 of them
DanJS
  • DanJS
oh forgot, here is a cheat sheet thing,
DanJS
  • DanJS
gl

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