Can anyone post how to calculate sin(18) by hand? i need the details. thanks.?
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
380391
Let alpha = arcsin 6x\nThen sin(alpha) = sin(arcsin 6x) = 6x\n\nNow note d(sin(alpha))/dx = d(sin(alpha))/d(alpha) * d(alpha)/dx (Chain Rule)\n\nd(6x)/dx = cos(alpha) * d(alpha)/dx\n6 = cos(alpha) * d(alpha)/dx\nTherefore, d(alpha)/dx = 6/cos(alpha)\n\nNow consider a right triangle with angle alpha < pi/2.  From before, we know sin(alpha) = 6x so we know the following:\n\nlength of leg opposite angle (a)/length of hypotenuse (c) = 6x\n\nso that...\n\na = 6cx\n\nUsing the Pythagorean Theorem, we get the length of the other leg b:\n\nb = sqrt(c^2 - 36c^2x^2) = c*sqrt(1 - 36x^2)\ncos alpha = b/c = sqrt(1 - 36x^2)\n\nTherefore d(alpha)/dx = 6/cos(alpha) = 6/sqrt(1 - 36x^2)\n\nNow you can proceed to solve using L'Hopital OR...\n-----------\nMake this problem more interesting and recall one of the first indeterminate forms you probably solved using the Rule (i.e. lim x-> 0 sin x/x = lim x -> 0 cos x/1 = 1/1 = 1).  This tells us that sin x ~ x for small angles x.  Therefore, arcsin x ~ x for small angles x so that that lim x -> 0 arcsin 6x/5x = lim x->0 6x/5x = lim x->0 6/5 = 6/5.  This can be made more precise with delta-epsilon definitions.
748469
The first thing I would do is rewrite both a and s in terms of h.\n\nThen you use the following rules to find the derivative.\n\n1.  Use the quotient rule to find the derivative of  sin(a)/s^2.  If you don't know the quotient rule -- look it up and memorize it.\n\n2.  The derivative of the sin is the cosin -- use the chain rule to get cos(a)*da/dh\n\n3.  The derivative of the bottom is  2*s * ds/dh (again using the chain rule).\n\nOnce you get the derivative, solve for zero.\n\nGood luck.
441926
180 - (32 + 44) = 180 - 76 = 104\n\na/sin(A) = b/sin(B) = c/sin(C)\n\n(a/sin(32)) = (20/sin(44))\nasin(44) = 20sin(32)\na = (20sin(32))/(sin(44))\n\nb/(sin(104)) = (20/(sin(44)))\nb = (20sin(104))/(sin(44))\n\na = about 15.25697\nb = about 27.93591\n\nIf you use the formula below\nc^2 = a^2 + b^2 - 2ab cos(C)\nYou will find out that the problem works out.
714757
(sinX + 1) = 0---> sinX = -1--->x = 3pi/2 + (2pi)n, radians, or x = 270 + 360n degrees, where n is any whole number including 0. \n\nThe first step was simple algebra.  In the second step, I just remembered that the sine is how far up on the unit circle that angle points, so -1 means it points straight down, which is 3/4 of a circle.  Adding a whole circle puts it right back where it started from.\n\ncosX + 1/2 = 0---> cosX = -1/2 ---> x = 2pi/3 or 4pi/3 + (2pi)n radians, 120 or 240 + 360n degrees.  \n\nAgain, the first step was simple algebra.  As for the second, my trig teacher made us memorize the sines/cosines of 30, 45, and 60 degrees, so I just know that the cosine of 60 degrees is 1/2.  Go around to the other side of the unit circle and the cosine of 120 degrees is -1/2.  Go down to the bottom of the unit circle, and the cosine of 240 degrees is also -1/2.
932480
sin(A+B)sin(A-B)/(cos²Acos²B)\n= (sinAcosB + cosAsinB)(sinAcosB - cosAsinB)/(cos²Acos²B)\n= (sin²Acos²B - cos²Asin²B)/(cos²Acos²B) (since (x + y)(x - y) = x² - y²)\n= sin²A/cos²A - sin²B/cos²B\n= tan²A - tan²B ← Option c)\n\nPlease note: sin(A + B) = sinAcosB + cosAsinB\nand sin(A - B) = sinAcosB - cosAsinB
754643
im taking Trig. try finding a homework helper web page. or go to the book that ur learning from web page because the majority of the times they have practice help on there.
842369
With these data a lot of angles fulfill that requirement; If  you have alpha first look at cos alpha, after divide by1.33  and look for theta.\n\nDid you not make a mistake. I suppose you mean sin and not cos\n\nSnell law uses sinus
759046
sin² x + cos² x = 1\n\nCenter a unit circle on the origin.  Let x be a point on the circle x units of distance around the circle from a starting point of (1,0). [so x is in radians].  Then the horizontal coordinate of x is sin x and the vertical coordinate is cos x, and so by Pythagorean theorem sin² x + cos² x = 1.
488283
I think that what you really want here is the tangent ratio. You know the slope of the line, right (hint, it is right there in the equation)? You know that the tangent ratio is a over b (where a and b are the non-hypotenuse sides of the triangle), right? You should be able to use that to figure out the tangent of the angle made by the line. Now all you have to do is figure out the angle that has that number as a tangent. That would be the "tan -1" (inverse tangent) function on your calculator.\n\nIf you are working from trig tables rather than a calculator, find the number in the second column of the tangent table that is closest to your tangent number then look in the first column for the angle.\n\nIf you are required to use sin and cosine remember your Pythagorean theorem and use it to find the hypotenuse.\n\nASIDE TO Drakestone: Your solution only finds the sine of the angle, not the angle itself. You need to apply "sin -1" to your answer to get the final answer.\n\n\nASIDE TO eternal...: You are wrong too. graph y=5x+3 and you will see that it is way too steep to be an 11 degree angle. You mixed up your opposite and adjacent values in calculating your tangent.
461039
sin2A = 2sinA.cosA\nSo,\nsin2A = 2*12/13*5*13\n      = 120/169\n\ngood luck!!
983394
Depends\n\nlim θ→π/2- (ie from below) tanθ = +∞\n\nlim θ→π/2+ (ie from above) tanθ = -∞ \n\nThis is because in the 1st quadrant tanθ >0 and in the second quadrant tanθ <0
623818
We can find angle B by subtracting the others from 180:\n\nB = 180 - 32 - 44\n= 104\n\nThe length of the sides can be found using the law of sines:\n\n(sin A)/a = (sin B)/b = (sin C)/c\n\nSo,\n\n(sin B)/b = (sin C)/c\n(sin 104)/b = (sin 44)/20\nb = 20(sin 104)/(sin 44)\n~ 27.94\n\n(sin A)/a = (sin C)/c\n(sin 32)/a = (sin 44)/20\na = 20(sin 32)/(sin 44)\n~ 15.26
1186234
Actually, when the answers come out as negative, it's calculating in radians. So the sine of 6 is negative, as it is actually calculating about 324 degrees.\n\n2nd+0 resets your calculator, but i don't recommend it.
716883
Trying for wow #2---\n\nR = .15 m\nω = 2π/T = 13.963 rad/sec\nA little vector diagram shows that tanθ = rω²m/mg = rω²/g\nbut r = Rsinθ, so tanθ = sinθ/cosθ = Rsinθω²/g  from which\n\n1/cosθ = secθ = Rω²/g = .15*13.963²/9.8 = 2.984 → θ = 70.42°\n\nYou get to do b)\nGood luck..
359761
When you need to use the HALF ANGLE formula, think of the given angle has HALF the ANGLE you need to use.  So:\n\nsin(105) = sin(210/2)\n\nThen use the formula using the angle 210.  And, since you know other ways to get the answer, you can check that you did it right!  (That's probably why you were given that angle.)
247689
Use analytical trig (hint: sin function).  That should give you the answer you are looking for.