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anonymous
 one year ago
Choose the point on the terminal side of 210°.
anonymous
 one year ago
Choose the point on the terminal side of 210°.

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phi
 one year ago
Best ResponseYou've already chosen the best response.1210 means start at the xaxis and go clockwise 210 degrees dw:1441116254558:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i know that but i dont know where to go from there

phi
 one year ago
Best ResponseYou've already chosen the best response.1if you want the (x,y) numbers, we need to know the length of the radius Probably they are assuming the radius is length 1

phi
 one year ago
Best ResponseYou've already chosen the best response.1210 is 30 "past" 180, so we can draw this triangle dw:1441116408316:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how did you get one for the radius

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it just always assumed

phi
 one year ago
Best ResponseYou've already chosen the best response.1It's a 306090 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
 one year ago
Best ResponseYou've already chosen the best response.1we can't answer the question unless we know r. But usually we use the "unit circle" when they ask questions like this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so how would i get the answer from that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it\[(\sqrt{3}, 1)\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1do you know the lengths of the sides of a 306090 triangle if you know the hypotenuse is 1?

phi
 one year ago
Best ResponseYou've already chosen the best response.1more generally, do you know about sin, cos ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i know about that but im just so confused how you got the 2 sides in the first place

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i just tried to find the 3rd side too and i dont think its right

phi
 one year ago
Best ResponseYou've already chosen the best response.1one 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
 one year ago
Best ResponseYou've already chosen the best response.1that 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
 one year ago
Best ResponseYou've already chosen the best response.1we 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 xaxis dw:1441117274941:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.1does this make sense so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes it does thank you

phi
 one year ago
Best ResponseYou've already chosen the best response.1so let's say we have this triangle dw:1441117338853:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you mean the coordinates?

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes. and notice the opposite side is also the "height" of the point above the xaxis. this is the y value of the (x,y) coords

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do we find x then

phi
 one year ago
Best ResponseYou've already chosen the best response.1what is the definition of cosine ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, and in this special case where we set the hyp=1 we have cos theta= adjacent

phi
 one year ago
Best ResponseYou've already chosen the best response.1notice the adjacent side is the distance along the xaxis

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do i use the pythagorean theorem

phi
 one year ago
Best ResponseYou've already chosen the best response.1we could, but we could use cos 30 = x people generally memorize this value

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what would that equal

phi
 one year ago
Best ResponseYou've already chosen the best response.1sqr(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
 one year ago
Best ResponseYou've already chosen the best response.1also, drill into your head the idea that cos = x sin = y (for a UNIT circle)

phi
 one year ago
Best ResponseYou've already chosen the best response.1now , 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
 one year ago
Best ResponseYou've already chosen the best response.1if we measure the angle "normally" from the positive xaxis 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 xaxis) we know it is +0.5

phi
 one year ago
Best ResponseYou've already chosen the best response.1for more help, see https://www.khanacademy.org/math/trigonometry/unitcircletrigfunc/Trigunitcircle/v/unitcircledefinitionoftrigfunctions1
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