A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Choose the point on the terminal side of -210°.

  • This Question is Closed
  1. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    -210 means start at the x-axis and go clockwise 210 degrees |dw:1441116254558:dw|

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i know that but i dont know where to go from there

  3. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if you want the (x,y) numbers, we need to know the length of the radius Probably they are assuming the radius is length 1

  4. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    210 is 30 "past" 180, so we can draw this triangle |dw:1441116408316:dw|

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how did you get one for the radius

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it just always assumed

  7. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It's a 30-60-90 triangle, so (if you learned this) the opposite side (which is the "y" value) is 1/2 of the hypotenuse if the radius is 1 , then y= 0.5 x = \( \sqrt{3} \cdot \text{ opposite side} = \frac{\sqrt{3}}{2}\)

  8. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we can't answer the question unless we know r. But usually we use the "unit circle" when they ask questions like this

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so how would i get the answer from that

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it\[(-\sqrt{3}, 1)\]

  11. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you know the lengths of the sides of a 30-60-90 triangle if you know the hypotenuse is 1?

  12. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    more generally, do you know about sin, cos ?

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i know about that but im just so confused how you got the 2 sides in the first place

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i just tried to find the 3rd side too and i dont think its right

  15. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    one step at a time. Let's say we have a unit circle (which means r=1) and we pick a random spot on the circle |dw:1441117005906:dw|

  16. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that is an example with 2 different spots notice that the (x,y) coordinates of a point are also the lengths of the sides (x is the horizontal side, and y is the vertical side) to make a triangle, we draw in a line from the point to the origin. |dw:1441117192063:dw|

  17. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we have a right triangle. the hypotenuse will always be 1 (it is the radius) we will always measure the angle up (or down) from the x-axis |dw:1441117274941:dw|

  18. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    does this make sense so far?

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes it does thank you

  20. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so let's say we have this triangle |dw:1441117338853:dw|

  21. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you know the sin 30º ?

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    which is 0.5?

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you mean the coordinates?

  24. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes. and notice the opposite side is also the "height" of the point above the x-axis. this is the y value of the (x,y) coords

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how do we find x then

  26. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is the definition of cosine ?

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    adj/hyp

  28. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, and in this special case where we set the hyp=1 we have cos theta= adjacent

  29. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    notice the adjacent side is the distance along the x-axis

  30. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do i use the pythagorean theorem

  31. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we could, but we could use cos 30 = x people generally memorize this value

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what would that equal

  33. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sqr(3)/2 They expect you to memorize sin, cos and tan of 0, 30, 45, 60, and 90 degrees so put that on your list of things to do.

  34. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    also, drill into your head the idea that cos = x sin = y (for a UNIT circle)

  35. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now , I said cos 30 = sqr(3)/2 but we have to be careful. the x value of the point is on the left side , so it is negative. the point is at \[ \left( - \frac{\sqrt{3}}{2} , \frac{1}{2} \right)\]

  36. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if we measure the angle "normally" from the positive x-axis |dw:1441117944457:dw| the angle is 150º and your calculator will give the answer cos 150= -0.866.. (which is decimal for - sqr(3)/2) and sin(150) = 0.5 (decimal for 1/2) but without a calculator, we figure out the reference angle 30 use our memorized value cos 30= sqr(3)/2 , then look at the picture and see we want the x value (the cos ) to be negative, so -sqr(3)/2 and sin 30 = 0.5, and because we are on the positive (above the x-axis) we know it is +0.5

  37. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    for more help, see https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circle-definition-of-trig-functions-1

  38. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.