anonymous
  • anonymous
how do i find sin and cos from an angle like -3pi/4
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
phi
  • phi
I would change it to degrees (easier for me to think about) then sketch the angle on graph paper
phi
  • phi
Then find the "reference angle" which will be the acute angle it makes with the x-axis
anonymous
  • anonymous
i know it equals -135 degrees but i am confused if the cos and sign would be (-sqrt2/2,sqrt2/2) or (-sqrt2/2,-sqrt2/2) because wouldnt you just got the clockwise when dealing with negative degrees and 135 degrees would put you in the third quadrant?

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anonymous
  • anonymous
**-135 degrees would put you in the third quadrant?
phi
  • phi
yes, -135 means start at the positive x-axis and go clockwise |dw:1378247650969:dw|
anonymous
  • anonymous
referecne angle beingn 45
anonymous
  • anonymous
i see i see, so then it would in fact be (-sqrt2/2,-sqrt2/2)?
phi
  • phi
use the sign of the x and y coordinates to figure out the signs as you can see, y is negative, so sin will be -y/hyp (and the hyp is always positive) you get sin(-135) = - sin(45) = -sqr(2)/2
phi
  • phi
yes
anonymous
  • anonymous
i see thank you very much
anonymous
  • anonymous
also is there anyway you could show me how to get cos and sin from and angle? like 45 degrees, is there a formula?
phi
  • phi
There are special cases which you should memorize (most angles you need a calculator to find their sin, cos or tan)
phi
  • phi
I assume you know 0, 30, 45, 60, 90 see http://math.tutorvista.com/trigonometry/sine-cosine-tangent-table.html
anonymous
  • anonymous
yeah i do but i was wondering for like a special angle more like 178, you know just in case i forget exactly what they are i can figure it out with algebra
phi
  • phi
no easy way, which is why (before calculators) they had big tables
anonymous
  • anonymous
i see, well thank you for your help, helps more than my instructor lol
phi
  • phi
See http://www.khanacademy.org/math/trigonometry/basic-trigonometry/unit_circle_tut/v/unit-circle-definition-of-trig-functions-1 for more info. If we define the trig functions on the unit circle (see video), we can identify x with the cosine and y with the sine
anonymous
  • anonymous
thanks man. How would you find the cos and sin of 220 with a radius of 15 on a cacluator. i know sin and cos but i dont know how you input a different radius
phi
  • phi
What exactly is the question ? cos(220º) is a number and you don't need to know a radius to find it. If you are looking for the length of an arc, that is something else
anonymous
  • anonymous
find the cooordinates of a point on a circle with radius of 15 corresponding to an angle of 220
phi
  • phi
if you draw a circle with radius 15, and sketch in 220º, and make a right triangle you will get a right triangle with a reference angle of 40º in the 3rd quadrant cos(40) = x/r (but you have to pick the correct sign) and x = r*cos(40) But if you use a calculator, it's easier to use 220º, because the calculator will come up with the correct sign cos(220) = x/r solve for x: x= r*cos(220)
anonymous
  • anonymous
oh i see, thank you. so when you have 30 degrees and the sin and cos are (sqrt3/2,1/2) are those not the (x,y) coordinates?
phi
  • phi
(sqrt3/2,1/2) are those not the (x,y) coordinates? They are the (x,y) coordinates of a point on the unit circle, with radius = 1
anonymous
  • anonymous
is that because it is all over 1? so would it be (sqrt3/2/15,1/2/15) if the radius was 15 theoretically speaking?
phi
  • phi
the sin, cos, tan are ratios sin(A) = adjacent / hypotenuse the sin(30) will always be 1/2 But if you are interested in an (x,y) pair on a circle, the x or y will change depending on the radius
anonymous
  • anonymous
so all reference angles always have the same sin and cos not matter the radius?
phi
  • phi
so would it be (sqrt3/2/15,1/2/15) depends what "it" is... if you want the coordinates of a point on the circle with radius 15, at an angle of 30º, the x will be 15 * cos(30)= 15/2 sqr(3)
anonymous
  • anonymous
so cos =x/r, could it be expressed as (sqrt3/2)/15?
anonymous
  • anonymous
actaully i get what your saying, sqrt3/2 is the cos and x/r=sqrt3/2?
anonymous
  • anonymous
its all starting to make sense now......
phi
  • phi
yes, your last two posts are making sense.
anonymous
  • anonymous
i get it now, thanks for all the help today i now understand sin and cos lol

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