anonymous
  • anonymous
Choose the point on the terminal side of -210°.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
phi
  • phi
-210 means start at the x-axis and go clockwise 210 degrees |dw:1441116254558:dw|
anonymous
  • anonymous
i know that but i dont know where to go from there
phi
  • phi
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

Looking for something else?

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

More answers

phi
  • phi
210 is 30 "past" 180, so we can draw this triangle |dw:1441116408316:dw|
anonymous
  • anonymous
how did you get one for the radius
anonymous
  • anonymous
is it just always assumed
phi
  • phi
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 = \( \sqrt{3} \cdot \text{ opposite side} = \frac{\sqrt{3}}{2}\)
phi
  • phi
we can't answer the question unless we know r. But usually we use the "unit circle" when they ask questions like this
anonymous
  • anonymous
so how would i get the answer from that
anonymous
  • anonymous
is it\[(-\sqrt{3}, 1)\]
phi
  • phi
do you know the lengths of the sides of a 30-60-90 triangle if you know the hypotenuse is 1?
phi
  • phi
more generally, do you know about sin, cos ?
anonymous
  • anonymous
yes i know about that but im just so confused how you got the 2 sides in the first place
anonymous
  • anonymous
i just tried to find the 3rd side too and i dont think its right
phi
  • phi
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|
phi
  • phi
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|
phi
  • phi
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|
phi
  • phi
does this make sense so far?
anonymous
  • anonymous
yes it does thank you
phi
  • phi
so let's say we have this triangle |dw:1441117338853:dw|
phi
  • phi
do you know the sin 30º ?
anonymous
  • anonymous
which is 0.5?
anonymous
  • anonymous
you mean the coordinates?
phi
  • phi
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
anonymous
  • anonymous
how do we find x then
phi
  • phi
what is the definition of cosine ?
anonymous
  • anonymous
adj/hyp
phi
  • phi
yes, and in this special case where we set the hyp=1 we have cos theta= adjacent
phi
  • phi
notice the adjacent side is the distance along the x-axis
anonymous
  • anonymous
do i use the pythagorean theorem
phi
  • phi
we could, but we could use cos 30 = x people generally memorize this value
anonymous
  • anonymous
what would that equal
phi
  • phi
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.
phi
  • phi
also, drill into your head the idea that cos = x sin = y (for a UNIT circle)
phi
  • phi
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 \[ \left( - \frac{\sqrt{3}}{2} , \frac{1}{2} \right)\]
phi
  • phi
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
phi
  • phi
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

Looking for something else?

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