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anonymous

  • one year ago

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.

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  1. jdoe0001
    • one year ago
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    \(\begin{array}{cccllll} (1&,&-1)\\ x&,&y \end{array}\qquad hypotenuse=r=\sqrt{x^2+y^2}\impliedby \textit{pythagorean theorem} \\ \quad \\ \quad \\ sin(\theta)=\cfrac{y}{r} \qquad % cosine cos(\theta)=\cfrac{x}{r} \qquad % tangent tan(\theta)=\cfrac{y}{x}\impliedby \textit{find "r", and plug and chug}\)

  2. anonymous
    • one year ago
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    Mg I know you from my school :/

  3. anonymous
    • one year ago
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    @carsonce I'm kinda homeschooled so...

  4. DanJS
    • one year ago
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    Draw the thing first

  5. DanJS
    • one year ago
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    'standard' - relative to the +x axis i believe

  6. DanJS
    • one year ago
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    |dw:1443138414973:dw|

  7. DanJS
    • one year ago
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    4th quadrant

  8. DanJS
    • one year ago
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    You see how the components of that line are at right angles to the x and y axis?

  9. DanJS
    • one year ago
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    |dw:1443138594122:dw|

  10. anonymous
    • one year ago
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    yeah

  11. DanJS
    • one year ago
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    you have right triangles with side lengths of 1

  12. DanJS
    • one year ago
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    |dw:1443138683435:dw|

  13. DanJS
    • one year ago
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    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

  14. DanJS
    • one year ago
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    Example \[\sin(\theta) = \frac{ 1 }{ \sqrt{2} }\] \[\theta =\sin^{-1} [\frac{ 1 }{ \sqrt{2} }] = 45\]

  15. DanJS
    • one year ago
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    So the angle theta is 45, but recall you are in the 4th quadrant

  16. anonymous
    • one year ago
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    oooooh okay I see now

  17. DanJS
    • one year ago
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    So the theta is actually from +x CounterClockWise to that terminal side`

  18. DanJS
    • one year ago
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    360-45 = 315

  19. anonymous
    • one year ago
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    Thank you for your assistance. I'm usually pretty good at math, but trig is tripping me up so much...

  20. DanJS
    • one year ago
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    The sin value of theta and (360-theta) are the same, (the y value on the unit circle point)

  21. DanJS
    • one year ago
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    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

  22. DanJS
    • one year ago
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    each point ON the unit circle of radius 1 centered at the origin, is (x , y) = ( cos(angle), sin(angle) )

  23. DanJS
    • one year ago
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    i fyou are that far yet

  24. anonymous
    • one year ago
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    Ah okay

  25. DanJS
    • one year ago
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    These may help, solved probs and stuff https://drive.google.com/folderview?id=0B1YZD9uzvB5TfnkzNzg5LU54VC1zUENBNHZoWlUxYXk1OXQtNklXdVVtZnA1T3c4X3hMMWM&usp=drive_web#list

  26. DanJS
    • one year ago
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    the last 5 of them

  27. DanJS
    • one year ago
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    oh forgot, here is a cheat sheet thing,

  28. DanJS
    • one year ago
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    gl

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