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Question About Unit Circle (CircularFunction) of a Trig Func

  1. Oct 20, 2015 #1
    Please take a look below example (the attached image below).

    How do I know that the angle ##\sin (\frac{7π}{4})## is corresponds to the coordinates ##(\frac{\sqrt {2}}{2}, -\frac{\sqrt{2}}{2})##?

    I know that ##\frac{7π}{4}## is 315°.

    circ_func.png
     
  2. jcsd
  3. Oct 20, 2015 #2

    BvU

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    Did you draw a unit circle and mark e.g. the ##7\pi \over 4## angle ?
     
  4. Oct 20, 2015 #3
    Should I?
     
  5. Oct 20, 2015 #4

    BvU

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    Yes
     
  6. Oct 20, 2015 #5

    Ssnow

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    subtract ## 2\pi## that is ##\frac{7}{4}\pi -2\pi=\frac{7-8}{4}\pi=-\frac{\pi}{4}##...
     
  7. Oct 22, 2015 #6

    HallsofIvy

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    If you draw a line from (0, 0) with length 1 and making angle [itex]\theta[/itex] with the x-angle and drop a perpendicular to the x-axis, then the distance to the foot of that perpendicular, along the x-axis is the "near side" of a right triangle with angle [itex]\theta[/itex] and hypotenuse 1. Similarly, the length of the perpendicular, parallel to the y-axis, is the "opposite side".
     
  8. Oct 22, 2015 #7
    Well, I think any high school teacher I knew when I was teaching would have a simple answer:

    Memorize the unit circle (which isn't so hard to do if notice the angular symmetries and remember the mnemonic device All Students Take Calculus in order to remember the signs).
     
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