How can I solve an equation involving double and half angles?
484958
sin 2x=2 sinx . cos x\ncos 2x=(cos x)^2-(sin x)^2\ncos 2x=2 (cos x)^2 -1\ncos 2x=1- 2 (sin x)^2\ntan 2x=(sin 2x)/(cos 2x)\n\nor you can \nsin 2x=1\nlet 2x=y\nsin y=1\ny=90 degree + 360 degree\n2x=90 degree + 360 degree\nx=45 degree + 180 degree\nso x={45,225,....}degree\n\ntan x+cot x=2/sin 2x:\ntan x+cot x\n=(sin x/cos x )+(cos x/sin x)\n=((sin x)^2+(cos x)^2)/(sin x . cos x)\n=1/(sin x . cos x)\n=2/2(sin x . cos x)\n=2/sin 2x\nso it is an identity
784670
The trick is that you can do the same thing to both sides of an equation:\n\n1. Divide both sides by W: L = A/W\n\n2. Subtract 32 and multiply by 5/9: C = (F - 32) * 5 / 9\n\n3. Multiply both sides by 2 and divide by b: h = 2A/b\n\nSimple steps, once you have the hang of it.
932500
I don't know any good math websites but I do know how to solve this.  b would be the side adjacent to the 40 degree angle and a is the side opposite it.\n\nTangent = opposite leg/adjacent leg so\ntan 40 = 15/b\n\nb tan 40 = 15\n\nb = 15 / tan 40
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
217108
You have a right triangle with legs a and b, and hypotenuse c.\na+b=8\nc=6\n\na^2 + b^2 = c^2 = 36\n\nSquare both sides of a+b=8\na^2 + 2ab + b^2 = 64\n\nSubtract previous equation:\n\n2ab = 64 - 36 = 28\n\nab = 14\n\n(1/2)*ab = 7\n\nArea = 7.
129693
1) square both sides\n\n2) then make trig substitutions to get same 'variable'. Get sin^2[x] throughout equation. \n\ncos^2[x] + sin^2[x] = 1, so\n\n1 - cos^2[x] = sin^2[x].\n\n3) sin[x] cos[x] = ...\n\n4) Set equal to zero\n\n5) Solve.
783875
Complement angles equal 90 degrees, therefore\n\n\n90 = larger (x) + smaller (x-25)\n\n90 = x + x - 25\n\n90 = 2x - 25  (add 25 to both sides)\n\n90 + 25 = 2x   or 115 = 2x\n\ndivide both sides by 2\n\nx = 57.5 degrees (larger angle)\n\nsmaller angle = larger angle - 25\n\nsmaller = 57.5 - 25 = 32.5 degrees\n\nAnswer 32.5 degrees
22859
Subract the two terms on the left giving:\n-2t < 16\n\nAdd 2t to both sides giving\n0 < 16 + 2t\n\nSubtract 16 from both sides\n\n-16 < 2t\n\nDivide both sides by 2\n\n-8 < t
109151
It looks like your equation got cut off, but I think you were writing\n\nR = (V^2/2g)(sin (2 theta) +sin (2 theta))\n\nwhich can be immediately simplified, by adding the sin (2 theta) terms, as \n\nR= (V^2/2g )(2)(sin(2 theta) = (V^2/g )sin (2 theta)\n\nwhich is the formula that the other correspondent already gave.  To solve it, simply multiply both sides by g, divide by V^2, and you get \n\n(R g)/v^2 = sin (2 theta)\n\n[Arcsin (Rg/V^2) ]/2 = theta
928764
You would just do 180-56 to equal 124 degrees\n\nsupplementary angles add up together to equal 180 degres or a straight line
623793
Here, you need to use the law of cosines, because you don't have and angle-opposite side pair.\n\nd^2 = e^2 + f^2 - 2de*cos(D)\n\nPlug in the values to solve for d^2 then take the square root to find d. Use your calculator.
21860
Let's call these angles A and B.  And let's call C the adjacent angle in the middle of these two angles.\n\nThen we will have:\n\nA + C = 180\nB + C = 180\n\nAs a result, A = B = 180 - C
375577
Well you really can't use a half angle identity unless you have a function in from of the angle.\n\n19pi/12 equals 285 degrees, just FYI.
948099
+90° rotation (ie 90° anticlockwise)\nA = (0, -5) → (-5, 0)\nB = (1, 9) → (-9, 1)\nC = (8, 9) → (-9, 8)\nD = (-3, -1) → (1, -3)\n\n-90° rotation (ie 90° clockwise)\n\nA = (0, -5) → (5, 0)\nB = (1, 9) → (9, -1)\nC = (8, 9) → (9, -8)\nD = (-3, -1) → (-1, 3)
896553
4x^2+8x-x-2\n(4x-1)(x+2)
233924
48x^2y+20xz+20xy+5z\nI switched the position of the two middle terms.\n48x^2y+20xy+20xz+5z\n4xy(12x+5)+5z(4x+1)
166573
:)\nNice trick question.\nYou should mention that the whole 'equations' reads:\n2 times (pi) radians = 360 degrees (measuring angles).\ntherefore (pi) radians equales 180 degrees (half circle)\nBut the number (pi) is same old 3.14......