How Do You Convert From Degrees To Radians?? S.O.S!!?
965129
One way to convert degrees into radians is to set up a proportion.  180 degrees is equal to pi radians (360 degrees= 2 pi radians).\n\nHere is an example of how to convert 30 degrees.\n\n180/ pi = 30/x\nUsing cross multiplication, you have 180x = 30 pi.\nAfter dividing both side by 180 you have x = 30 pi/180.\nThis can be simplified to 3 pi/18 = pi/6.\n\nSo for your example of 150 degrees.  The method is similar.\n\n180/ pi = 150/x\nCross multiplication.  180x =150pi.\nx = 150 pi/180.\nx = 15 pi/18   Now divide the top and bottom by three  = 5 pi/6\n\nGood luck with your exam and I hope this helps!
850990
In this case involving trigonometric operation on angles, you will need to carry the error over to your operation results. What I mean by that is:\n\nYou have an angle known only to 1 degree of precision, i.e.\n\nθ = 32° ± 1°\n\nTherefore, when you compute Cos (32°) = 0.848 \n\nYou will also need to perform the trig operation including the error:\n\nCos(31°) = 0.857 and Cos(33°) = 0.839\n\nSo your measurement is 0.848 ± 0.009 or 0.85 ± 0.01 depending on how many significant digits you want to keep.
730213
Let u, v be the rotated x, y, rotated counter-clockwise by an angle t.\n\nThen x = u*cos(t) + v*sin(t), and y = -u*sin(t) + v*cos(t).\n\nPlug these into the equation (abbreviating c=cos(t), s=sin(t))\n\n(uc+vs)^2 + 4(uc+vs)(vc-us) + 4(vc-us)^2 + (5*sqrt(5))(vc-us) + 5\n= u^2*c^2 + 2*uvcs + v^2*s^2 + 4*uvc^2 + 4*v^2*cs - 4*u^2*cs - 4*uv*s^2 + 4*v^2*c^2  - 8*uvcs + 4*u^2*s^2 + 5*sqrt(5)(vc-us) + 5\n= u^2(c^2-4cs+4s^2) + uv(2cs + 4c^2 - 4s^2 - 8cs) + v^2(s^2 + 4cs + 4c^2) + 5*sqrt(5)(vc-us) + 5\n\nso to eliminate the xy term, we must have 2cs + 4c^2 - 4s^2 - 8cs = 0, but 2cs = sin(2t) and c^2 - s^2 = cos(2t), so we have\n4cos(2t) = 3sin(2t), or tan(2t) = 4/3, so t = arctan(4/3)/2 = 0.4636 radians.\n\nThe resulting equation is 5v^2 - 5u + 10v + 5 = 0.
1175205
In a full circle there are 360 degrees. \nEach degree is split up into 60 parts, each part being 1/60 of a degree.  These parts are called minutes. \nEach minute is split up into 60 parts, each part being 1/60 of a minute. These parts are called seconds. \n\nThe size of an angle could be stated this way: 40 degrees, 20 minutes, 50 seconds.\nHow could you state the above as an angle using common decimal notation? The angle would be this many degrees, (* means times.):\n\n40 + (20 * 1/60) + (50 * 1/60 * 1/60) \n\nThat is, we have 40 full degrees, 20 minutes - each 1/60 of a degree, and 50 seconds - each 1/60 of 1/60 of a degree.\n\nWork that out and you will get a decimal number of degrees.  It's 40.34722...\n\nGoing the other way is a bit more difficult. Suppose we start with 40.3472 degrees. Can we express that in units of degrees, minutes, and seconds?\n\nWell, first of all there are definitely 40 degrees full degrees. That leaves 0.3472 degrees.\n\nSo, how many minutes is 0.3472 degrees? Well, how many times can 1/60 go into 0.3472? Here's the same question: What is 60 times 0.3472?  It's 20.832. So, there are 20 complete minutes with 0.832 of a minute remaining.\n\nHow many seconds are in the last 0.832 minutes. Well, how many times can 1/60 go into 0.832, or what is 60 times 0.832? It's 49.92, or almost 50 seconds.\n\nSo, we've figured that 40.3472 degrees is almost exactly equal to 40 degrees, 20 minutes, 50 seconds.\n\n(The only reason we fell a bit short of 50 seconds is that we really used a slightly smaller angle in this second half of the calculation explanation.  In the original angle, 40.34722... degrees, the decimal repeats the last digit of 2 infinitely, so, the original angle is a bit bigger than 40.3472.)
760142
multiply the degrees by pi and divide by 180\ndegree*pi/180=radians
610173
Radians are based on pi.  A radian is equivalent to 1/(2pi).  Because it is just a ratio of another constant, it isn't based on a physical standard unlike feet, meters, etc.\n\nIt's just like degrees.  A degree is 1/360th of a complete circle, but nobody needs to define 360 with a physical object.  We all know what 360 is.  Similarly we know what 2pi is (it's the circumference of a unit circle).
1041436
I got  the first part. just get the cosx by itself. then you wind up with the cosx = -(the square root of 2/2)\nwhich is 225+360n and 315 +360n(in degrees)\nSorry i can't help you on the other one. Good luck, just keep trying new things with it, would be my advice.
546529
1. Make sure the angle of interest is in radians.  Radians are the "natural" (non)-units of angles, because they relate the angle measurement to the length of arc the angle cuts off on a unit circle.  So 2*Pi radians are equivalent to 360 degrees.  Basically, if you have that sucker in degrees, multiply it by 2 * Pi / 360.  Unit conversion is done. \n \n2. Make sure the angle is between -Pi and Pi.  Because sine is a periodic function, with period 2*Pi, just subtract or add 2*Pi enough times to get the angle between those two points.\n\nnow for the meat of the problem:\n\nsin(x) = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - ... + \n+ (-1)^(n-1)*x^(2n-1)/(2n-1)! + ...\n\nExample: sin(15)\n\nStep 1: 15 degrees = 15*(2*Pi/360) radians = Pi/12 radians \n \nStep 2: I need Pi/12 in decimal (let's see, Pi=3.14159 (memorize that much, it's pretty easy... "Pi when calculating sine, 3 point 1 4 1 5 9!")) \nPi/12 approx = .261799 (we only had 6 sig figs, so we can't add any more than that) \n \nNow to the series: \n         first term:  x=.261799 \n         1st estimate: .261799 \n         second term: -x^3/3! = -.0029905  \n         2nd estimate: .258809 \n         third term: x^5/5! = .0000102     \n         3rd estimate: .258819 \n         fourth term: -x^7/7! = -.167*10^-7  \n         stop here - past precision\n\nThe answer is positive \nsin(15) = 0.258819\nsin(18) = 0.309017
275762
cos(315)degrees=cos(360-45degrees)\n               =cos 45degrees\n               =1/root2
1041132
For r = cos theta:\n\nAt first ignore complications like r = 0 or r negative.  Then you can say that r = cos theta is sqrt(x^2 + y^2) = x / sqrt(x^2 + y^2) or x^2 + y^2 = x which you can manipulate to x^2 - x + 1/4 + y^2 = 1/4 or\n\n(x - 1/2)^2 + y^2 = (1/2)^2\n\nwhich is a circle with center (1/2, 0) and radius 1/2.  Then check whether r = 0 or r < 0 add anything else to that (my guess would be no).\n\nFor length of r = 1 - cos theta.\n\nHere r varies in [0, 2] so there is no r < 0 case to worry about.  The length will just be the integral from theta = 0 to 2 pi of ds / d(theta) where ds^2 = (r d(theta))^2 + (dr)^2 or ds / d(theta) = ((1 - cos theta)^2 + (sin theta)^2) (d(theta))^2.
34052
I do not know a preprogrammed utility to do this, but can point you in the direction that you might need to go.  See the reference below for the math and an on-line converter:
1054686
Job one, convert everything to trig functions of a single angle, namely x.\n\nsin2x=2sinxcosx\ncos2x=cos^2(x)-sin^2(x)=2cos^2(x)-1=1-2sin^2(x)\n\nThen substitute in and simplify:\n2sinxcosx+2(2cos^2(x)-1)=1+sinx-4cosx\n2sinxcosx+4cos^2(x)-2-1-sinx+4cosx=0\n4cos^2(x)+2sinxcosx-sinx+4cosx-3=0\n\nFactor this into:\n(2cosx-1)(2cosx+sinx+3)=0\n\nset each parantheses equal to zero\n2cosx-1=0   \ncosx=1/2\nx=arccos(1/2)\nx={pi/3, 5pi/3} + 2pi*n  where n=0,1,2....\n\nAnd\n\n2cosx+sinx+3=0\n\nSolved numerically gives imaginary solutions of\n{-i*ln((-2/5)-(i/5),-i*ln(-2-i)}\n\nSolved....
675696
I agree with changing Cot(Theta) into Cos(Theta)/Sin(Theta)\n\nsqrt(3)*Cot(Theta) = 2*Cos(Theta)\n\nsqrt(3)*Cos(Theta)/Sin(Theta) = 2 * Cos(Theta)\n\nsqrt(3)/2 = Sin(Theta)\n\nTheta = pi/3 and 2pi/3, or 60 degrees and 120 degrees.
72362
I forgot how to do those, but it's some sort of trig identity isn't it?  Like\n\nsqrt (1-tan [x])\n\nProbably not though.
535427
To do this, you have to do sin^-1 * decimal. Because Yahoo Answers only displays up to .0145, I'll do sin^-1 * .0145, which would be about 0.8308
124161
Degrees \nor Radians (used in higher classes mostly; pi rad = 180 deg)\nor steradians (used to measure solid angle)
501191
There is a formula...but this is much easier\n\nhttp://www.onlineconversion.com/temperature.htm