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I would change it to degrees (easier for me to think about) then sketch the angle on graph paper
Then find the "reference angle" which will be the acute angle it makes with the x-axis
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?
**-135 degrees would put you in the third quadrant?
yes, -135 means start at the positive x-axis and go clockwise |dw:1378247650969:dw|
referecne angle beingn 45
i see i see, so then it would in fact be (-sqrt2/2,-sqrt2/2)?
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
i see thank you very much
also is there anyway you could show me how to get cos and sin from and angle? like 45 degrees, is there a formula?
There are special cases which you should memorize (most angles you need a calculator to find their sin, cos or tan)
I assume you know 0, 30, 45, 60, 90 see http://math.tutorvista.com/trigonometry/sine-cosine-tangent-table.html
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
no easy way, which is why (before calculators) they had big tables
i see, well thank you for your help, helps more than my instructor lol
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
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
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
find the cooordinates of a point on a circle with radius of 15 corresponding to an angle of 220
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)
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?
(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
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?
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
so all reference angles always have the same sin and cos not matter the radius?
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)
so cos =x/r, could it be expressed as (sqrt3/2)/15?
actaully i get what your saying, sqrt3/2 is the cos and x/r=sqrt3/2?
its all starting to make sense now......
yes, your last two posts are making sense.
i get it now, thanks for all the help today i now understand sin and cos lol