Why sin11 is so nearly to one?
98433
11 is nearly 3.5 pi, which means the sine value ought to be nearly -1 (at 0.5 pi, 2.5 pi, 4.5 pi etc. it is plus one, at 1.5 pi, 3.5 pi, 5.5 pi etc. it is minus one).
983185
Take the first few derivatives of sin -- it is cyclical and you will see a pattern.  After you see the pattern, you will be able to say exactly what the 53rd derivative is, without having to actually take the derivative 53 times!\n\n~ ♥ ~
864328
binary 11 is 3 decimal
1057214
The amplitude of the function is -2, or simply 2.  This is because the value of sin(...) ranges from [-1...1], inclusive.\n\nThe 3x affects the frequency, but not the magnitude.
610758
sin(2x) = 2sinxcosx is a trigonometric identity called the double angle identity. It was derived from another identity:\n\n   sin(x + y) = sinxcosy + cosxsiny\n \nhere x and y are two different angles but what if x = y\nreplace y with x to make all the equations in terms of x, thus the equation becomes:\n\n   sin(x + x) = sinxcosx + cosxsinx\n   \nnote that sinxcosx is also equal to cosxsinx, so simplifying the equation it becomes:\n\n  sin(2x) = 2sinxcosx or sin(2x) = 2cosxsinx
499903
it the way the math worked out, there are supposedely either 11 or 26 dimensions. this math is way beyond me, but the theory is still unproven so they may be any number.
686146
Why is 7 - 2 = 5? Because 5 + 2 = 7.\nWhy is arcsin (0) = 0? Because sin0 = 0.
523359
It's just a convention. That's the definition of the sine. Some things just are what they are.
649598
Because you have two possibilities\nit can be either sinx or -sinx (depends on the quadrant in which the angle is)\nthat's because of the definition of absolute value\n\nand yes, I now see that you have sin x^2 and not sin^2x- so those are completely different, \nsin^2x=sinx*sinx\nand sinx^2 is simply sinx^2, try any angle and you'll see the difference,\nso onlt sqrtsin^2x=sinx
951662
well the number to the utmost left gets added by 11 and in every row 1 gets added more than the previous row so if u see the difference between any two consecutive row is always 12 !!\nthts wat i thnk
861916
I can't see the rest of your question, but even numbers can be multiples of three. Like 6 (2x3). They are not mutually exclusive.
226513
csc(x) is the same as 1/sin(x) and sec(x) is the same as 1/cos(x) so the left side of the equation can be simplified to \n\nsin(x)sin(x) + cos(x)cos(x) \nor sin^2(x) + cos^2(x)    {"sin squared x plus cos squared x"}\n\nUsing the same steps, the right side of the equation becomes sin(x)/sin(x) or 1.\n\nSo the identity has been reduced to  sin^2(x) + cos^2(x) = 1 which is another common trigonometry identity!
662739
a function is like a machine. when u input a no into it..it gives u a product corresponding to that no. now two or more different inputs can generate the same product from the machine. it only means that the machine recognizes a special characteristic of THAT group of inputs and generates the output not according to the individual no but according to that special characteristic of that group of inputs. for example sin 0=0 also sin 360=0 also sin 720=0...here sin is the machine which takes the inputs as 0,360,720..and gives the result as  0...the common characteristic of this group of inputs is that all of them can be represented as 2n(360) where n is any integer...the sin function recognizes this characteristic and generates the result accordingly
1015891
Isn't it sinx divided by 6?\nSimple just cancel 'n' from the numerator and the denominator.\nU will be left with six=6
626033
I wanted to give a partial answer that wasn't presented elsewhere:\n\ne.g. Sine 10 deg =0.174, while cosine 80 deg= 0.174. how ironic is that?!!\n\nIt's not ironic at all.  If you have a right triangle, you know one angle is 90°, and the sum of all angles must be 180°, so the other two angles must add to 90.  You give sin 10°, so the other angle must be 80°.\nThe sin of any angle must be equal to the cos of its complementary angle (x and 90°-x are complementary), because of the definitions.  The side opposite the x angle is adjacent to the the 90°-x angle.\nThus sin 10° = cos 80°.
319082
RHS cot a - tan b \n= cos a/sina - sinb/cosb \n= cosacosb - sinasinb/sinacosb\n= cos(a+b)/sinacosb\n= LHS (proven)\n\nThe idea is to prove that both sides are the same.
916168
6 sin 2x != sin 12 x\n\nnow sin x = 6 sin 2x\nor sin x = 6(2 sin x cos x)\nor sin x = 12 sin x cos x\nor 12sin x cos x - sin x = 0\nor sinx(12cos x -1) = 0\nsin x = 0 or cos x = 1/12\n\nsin x =0 => x = npi\ncos x = 1/12 => x = 2npi +/- cos^-1(1/12)