Does the sin(5 π/4) equal the sin(-π/4)? Why?
144046
LHS:sin(-π/4) = -sin(π/4)  since sin(-x)=-sin(x)  (odd function)\n\nRHS:sin(5π+4) = sin(π +π/4) = - sin(π/4) since sin(π+x) = -sin(x) (the sin is -ve in the 3rd quardon)\n\nLHS=RHS\n\nsin(5π/4)=sin(-π/4)\n\nUsing the unit circle 5π/4 is a angle on the 3rd quadron having the same y component to this one of -π/4 on the 4th quadron\nThe symmetrie  proove the both 5π/4 and -π/4 have the same  -ve sine\n\nAs 3π/4 in the 2nd quadron and π/4 on the 1st quadron having the same +ve sine
843808
If sin A = x and sinB = -x  then \nA = .... , -4π - B, -3π + B, -2π - B, -π + B,.-B, π + B, 2π - B, 3π + B, 4π - B, .... \n= nπ + (-1)^nB (n is any integer)\n\nSo arcsin(x) - arcsin(-x) = nπ + (-1)^nB - B\n= nπ + ((-1)^(n) -1)B\n\nNo this looks too clumsy ....new strategy!!\n\nsinA + sinB = 0\nSo 2 sin(½(A + B))cos(½(A - B)) = 0\n\nThus sin(½(A + B)) = 0 or cos(½(A - B)) = 0\nie ½(A + B) = 0, ±π, ±2π, ±3π, .... , ±nπ, \nie A + B = ±2nπ\nie arcsinx + arcsin (-x) = ±2nπ\n\nOr ½(A - B) =  ±π/2, ±3π/2, ±5π/2, ... , ±(2n - 1)π/2\nSo A - B = ±(2n - 1)π\nSo arcsinx - arcsin(-x) = ±(2n - 1)π
860947
sqrt ( -1 * -1 ) doesn't equal sqrt(-1) * sqrt(-1).\n\nanother example:\n\nsqrt ( 5 * 5 ) = sqrt ( 25) = 5\n\nbut it doesn't equal sqrt(5) * sqrt(5) because this is an irrational answer..\n\nhope this helps
776748
sin(3pi/4)= 1/sqrt(2) = sin(pi/4) \ncsc(3pi/4)=csc(pi/4) = sqrt(2)\nacsc(sqrt(2))=pi/4\n\n4pi/3 just doesn't work.
1104345
That simply means that the fraction is negative and should be treated accordingly.  4/-5 is the same thing as -(4/5) any number divided by a negative number becomes a negative number.  This is a very very very simple concept and needs to be understood for any competency whatsoever in the field of mathematics.
1015200
Let a, b, and c be the lengths of the legs of a triangle opposite angles A, B, and C. Then the law of sines states that\na/(sinA)=b/(sinB)=c/(sinC)=2R,\n\nwhere R is the radius of the circumcircle.\n\nIn other words,\n\nIn any triangle, the ratios of the sides to the sines of the opposite angles are equal.
873429
cos5x = sinx\ncos5x = cos(pi/2 - x)\n5x = 2npi +- (pi/2 - x)\n6x = (4n + 1)pi/2   ,   4x= (4n-1)pi/2\nx= (4n+1)pi/12    ,  x = (4n-1)pi/8
814753
The x-intercepts are where y is zero, hence, crossing the x-axis.\ny = sin(pi/2x) + 1\nSet y = 0\nthen, sin(pi/2x) = -1\nSo what value of x will make sin()=-1\nWell, when the argument pi/2x is some multiple of pi/2, like 3pi/2, 7pi/2, into + then - infinity.  Let's see, we want 3, 7, 11,... on the positive side and -3, -7, -11,... on the negative side.  Thinking about it yields an odd number plus 4; an odd number is 2n+1, then adding 4, 2n + 5.  Let's try it:  for n=-1, 2n+5=3; for n=0, 2n+5=5; for n=1, 2n+5=7; and the same for the negative side.\nBack to the original argument of sine:\npi/2x = 2n+5 for n = -infinity to + infinity\n(2n+5)2x = pi\nx=pi/[2(2n+5)] for n =
142343
As the responses above show, the answer is -1.  However, this implies two remarkable results.\n\nResult #1 is that e^i*n*pi is equal to -1 where n is any odd number.  The reason for this is as follows:\nFrom Eulers identity (mentioned above) we know that \ne^i*x  = cos(x) + i*sin(x)  \nso, as a result\ne^i*n*pi = cos(n*pi) + i*sin(n*pi)\nbut note that when n is an odd number\ncos(n*pi) is always -1    and\nsin(n*pi) is always 0.\nso the sum is always -1.\n\nResult #2 is that we can rewrite e^i*pi = -1 as\ne^i*pi + 1 = 0\n\nThis gives us e, i, pi, 1 and 0, five of the most fundamental numbers of mathematics, in one tidy pakage!\n\nBeautiful indeed!
656507
Use the law of sines\n\nn/sin(N)=m/sin(M)\n\nso \n\nm = n*sin(M)/sin(N)\n\nPlug in the values and use your calculator.
749352
The sin of pi approaches 0 which makes the numerator 0.  One minus the cos of pi approaches 2.  Which makes the denominator 2.  This makes the limit 0/2 or 0 so none of the answers are correct so choice (e).
49580
NO WAY Why?\n\nF(t) = A Sin(wt)\n\nA called the magnitude : how high the sine function reach\nif A =1 the sine is between 1 and -1\nif A =5 the sine is between 5 and -5\n\nW = 2*pi*f where f is the frequency : how many period during 1 sec\nif w=1 f=1/(2pi) this means at t=2pi we will have one period\nsin(2pi)=sin(0), one period for each 2pi\nif w=2 >>> one period ecah pi\n\n\nSO when the function is expressed by the sum of many sines, many differents frequancies, impossible to regroup them in one frequency\n\nTHe basic frequency called fimdemental and the other frequencies called harmonics (mulpitles of fundemental)\n\nFourrier Series gives the magnitude of all harmonice of unregular from, BUT IT IS NOT POSSIBLE TO JOINT MORE THAN ONE FREQUENCY IN ONE TERM\n\nlike 3x^2+4x^5 since the powers are differents we can't sum or add them in one term
1159205
pair up the  opposite sines, for example sin(10) and sin(350) and add them:\nsin(10) + sin(350) = 0\nsin(20) + sin(340) = 0\n...\nuntil you only have sin(180) and sin(360) which both equal 0\n\nPS. I assumed you were using degrees (sexagesimal). Won't work in radians (RAD) or metric (decimal) angles.
814944
we can  Use the trig identity\nsin(a+b)=sin(a)cos(b) + sin(b)cos(a) \nand we have\n\n10[sin(w.t)cos(π/4) + sin(π/4)cos(w.t)] \nwhich can be simplified as\n 10[√(2)/2sin(w.t) + √(2)/2cos(w.t)]\n= 5(√2)[sin(w.t) + cos(w.t)] \n\n a=5√2\n b=5√2
640703
As the pi is present in both questions, it is generally written in radians and not degrees. So either:\na) change the mode of your calculator to radians or\nb) Multiply your radian value by 180 degrees and divide this by pi.\n\n1. cos 5/3 pi = cos300 = 0.5\n2. sin 7/4 pi = sin315 = -0.707 (or -1/SQRT2)
709530
let x=-pi, then y=3{sin(-pi+(pi/3))]=3{sin(-2pi/3)}= (- 3) (sqrt(3))/2)\nx=pi y=3sin(4pi/3)= (- 3) (sqrt(3))/2)
619339
It is symmetric about the line x = -3\nThis means that if you plug in -4, then you will get the same value when you plug in -2.\nSo you only have to plug in one of them.\nDo not foil it out.  It is easier the way it is written.\ny(-4) = (-4+3)^2 + 1\ny(-4) = 2\nThus, by symmetry y(-2) = 2\ny(-5) = (-5+3)^2 + 1\ny(-5) = 5\nThus, y(-1) = 5 by symmetry