2006-09-26 18:50:29 · 8 answers · asked by Anonymous in Education & Reference ➔ Homework Help
sinx=2sin(x/2)cos(x/2)=2sqrt(1-cos^2(x/2))cos(x/2)=.6
==>4(1-cos^2(x/2))cos^2(x/2)=.36
==>(1-cos^2(x/2))cos^2(x/2)=.09
==>cos^2(x/2)-cos^4(x/2)=.09
==>cosx=+-3/sqrt(10) and cosx=+-1/sqrt(10)
π/2 ≤ X ≤ 3π/2
==>cosx=-3/sqrt(10) and cosx=-1/sqrt(10)
If you don't give me 10 point I'll not answer your next question.(Choose me as best answer)
2006-09-26 19:06:10 · answer #1 · answered by Mamad 3 · 0⤊ 1⤋
The exact answer is cos(x/2) = 1/sqrt(10). The rationale follows.
First note that x has to be in the second quadrant (from pi/2 to pi) or else sin(x) would be negative. So the answer we seek must satisfy pi/4 <= x/2 <= pi/2.
sin(x)=6/10=2*sin(x/2)*cos(x/2) =2*sqrt[1-cos^2(x/2)]*cos(x/2)
or
3/10 = sqrt[1 - cos^2(x/2)] * cos(x/2)
Squaring both sides and rearranging gives
cos^4(x/2) - cos^2(x/2) + (9/100) = 0
or
( cos^2(x/2) - (9/10) ) * ( cos^2(x/2) - (1/10) ) = 0.
So cos(x/2) = (+/-) 3/sqrt(10) or cos(x/2) = (+/-) 1/sqrt(10).
Now test whether these possible solutions put x/2 in the range
pi/4 <= x/2 <= pi/2 (or 45 degrees <= x/2 <= 90 degrees)
corresponding to pi/2 <= x <= pi.
InvCos[1/sqrt(10)] ~= 71.565 degrees. This works.
InvCos[-1/sqrt(10)] ~= 108.435 degrees. Too big.
InvCos[3/sqrt(10)] ~= 18.435 degrees. Too small.
InvCos[-3/sqrt(10)] ~= 161.565 degrees. Too big.
2006-09-26 19:26:53 · answer #2 · answered by stumpy 2 · 0⤊ 1⤋
sin x=0.6, π/2 ≤ X ≤ 3π/2,
cos^2 x= 1-sin^2 x = 0,64 => cos x = -0.8 because between π/2 and 3π/2 cos is negative. cos x/2= √(1+cos x)/2 => cos x/2= √(1-0.8)/2=√0.2 ~0.44 cos x/2=+ 0.44 or-0.44
2006-09-26 20:22:41 · answer #3 · answered by suzanna_banana 3 · 0⤊ 0⤋
The gist of the communicate available (sorry, there are too many pages to provide each and every of the links) is that wands help to concentration the magic resident contained in the witch or wizard, yet wandless magic continues to be accessible, truly for extremely proficient human beings like Snape and Dumbledore. some examples ... Apparition Assuming one's Animagus variety (or Metamorphpagus) Accio (the Summoning appeal) Elves can do magic without using wands Lumos
2016-12-02 03:48:22 · answer #4 · answered by sawney 3 · 0⤊ 0⤋
It's been awhile, but wouldn't you just take that arcsin of 0.6 to get the value of X then plug it into cos (x/2)?
2006-09-26 19:02:15 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Sin x=0.6
x=35 deg
Cos x/2 = 0.95
2006-09-26 19:06:35 · answer #6 · answered by Fred 2 · 0⤊ 0⤋
Sin x=0.6
x=35 deg
Cos x/2 = 0.95
2006-09-26 18:52:01 · answer #7 · answered by lol 2 · 0⤊ 1⤋
0.83
2006-09-26 18:59:02 · answer #8 · answered by inventor 1 · 0⤊ 1⤋