More Trig help??? I Really need it!!? 10 pts!!?

My tutor told me that "π/3 on the unit circle is located at (1/2, √3/2). But when i say to take the SINE of π/3, that means you do opposite over hypotenuse, or in other words: y over r."

What does she mean? I am really confused. And i am afraid i am going to fail.....

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  • Anonymous
    9 years ago
    Favorite Answer

    Take the unit circle, x^2 + y^2 = 1, and draw a line from the center of the circle to some point on the circle. If θ is the angle made between the line connecting the origin to some point on the circle and the positive x-axis, then trigonometry gives:

    cosθ = x/1 = x and sinθ = y/1 = y.

    (Note that the "1" here is the radius of the circle. You can see why if you draw this out.)

    In general, for a circle of radius r, these are:

    cosθ = x/r and sinθ = y/r,

    due to the same reason as above (SOHCAHTOA).

    I hope this helps!

  • coreyA
    Lv 6
    9 years ago

    I understand that sin means y/r. When you are at this point in trig you aren't worried about that so much any more. π/3 on the unit circle (r =1) has the point (1/2, √3/2). If you were to draw a triangle whose hypotenuse was 1 and looked at the angle that is π/3 (60 degrees) sin(π/3) would be √3/2. When using the unit circle, learn to associate sin with y and cos with x. So at π/3, the x is 1/2 and y is √3/2. I hope this helps to clear things up a bit.

  • 9 years ago

    When you draw the angle π/3, or 60 degrees, you draw a line vertically to the x axis to form a right triangle. The sides of the triangle are the x and y values of π/3, so the bottom adjacent side is 1/2 and the opposite side is √3/2. Sine is opposite/hypotenuse (in this case this is also r) so it is (√3/2)/(1)= √3/2. The r value or hypotenuse is 1 because we are using the unit dircle.

    Source(s): Enriched pre calculus student
  • 9 years ago

    Pi/3 is 60 degress. On a unit circle 60 degrees is located at .5, √3/2

    here is how you find those .5 and √3/2.

    cos = x axis

    sin= y axis

    sin60=√3/2 which is your y value.

    cos60=.5 which is your x value

    Source(s): Took AP calc in HS
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  • 9 years ago

    if you are confused about the unit circle use this table.

    pi/6 pi/4 pi/3

    sine 1 2 3

    cos 3 2 1

    all the number have square roots over them and are over the number two. So the sine of pi/3 is sqrt3/2. The cosine of pi/6 is sqrt3/2. The tan of pi/3 is sqr3.

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