anonymous
  • anonymous
im having ahard time with this question by trial and error with your calculator, find the angle theta for which sin theta and theta differ by 5%. This calculation must be done in radians. when you have found theta, express it in degrees.
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
First, let's define percent difference. \[{\rm Percent~Difference} = {\rm difference \over maximum}\]where difference is the difference between \(\sin \theta\) and \(\theta\) and maximum is the value that has the greatest magnitude. Take a look here for more information on small-angle approximations. http://en.wikipedia.org/wiki/Small-angle_approximation \[0.05 = {|\sin(\theta) - \theta| \over \theta}\]Since \(\theta\) will be greater than \(\sin(\theta)\) for all values of \(\theta \gt 0\) There is no direct method to solve this. You're going to have to do a little guess and check. Might I recommend starting somewhere less than \(\theta \lt 1\)
anonymous
  • anonymous
umm can u tell me if 0.02 is right?
anonymous
  • anonymous
when i put in the radians i got 0.019

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anonymous
  • anonymous
I'm getting something close to 0.5 radians.
anonymous
  • anonymous
the way im doing is i set up it like this sintheta= 0.95(theta)
anonymous
  • anonymous
and my calculator is is in radians
anonymous
  • anonymous
Be careful with that expression. That assumes that theta must be 5% less than sin(theta). However, percent difference says that sin(theta) can be 5% less than theta. Since we know that sin(theta) < theta for all theta, lets use this expression. \[0.95 \sin \theta = \theta\]
anonymous
  • anonymous
sin (0.5) =0.479 radians 0.5/0.95=0.526
anonymous
  • anonymous
That looks like what I got.
anonymous
  • anonymous
Within 1%
anonymous
  • anonymous
so to get the degree do i just say 0.5 radians (180 degrees)/radians
anonymous
  • anonymous
\[\rm degrees = {180 \over \pi}\]
anonymous
  • anonymous
so its not 0.5 radians time 180 degrees/ radians
anonymous
  • anonymous
is the angle 90
anonymous
  • anonymous
Negative. The conversion is\[\rm degrees = {180 \over \pi}\] You should get approximately 28.5.
anonymous
  • anonymous
how canu please show me
anonymous
  • anonymous
Sorry. \[\rm degress = [radians] {180 \over \pi}\]
anonymous
  • anonymous
so 0.5 is not treated as radians because i thought it was 0.5pi(180/pi)
anonymous
  • anonymous
the question asks the difference betwene theta and sin theta should only be 5 percent but in my situation ios only 1
anonymous
  • anonymous
I think I'm confused as to where you are confused. We solved for theta such that a 5% difference had to be satisfied.
anonymous
  • anonymous
okay just to make sure i calculated properly i did o.526-0.479=0.47x100 =5percent
anonymous
  • anonymous
so the difference is 5 percent
anonymous
  • anonymous
i read the lin u gave me but im still not sure how u knew that theta had to be leass than one (srry eashmore for bithering u )
anonymous
  • anonymous
I know because I've used this approximation several times. Also note that this approximation is called the "small-angle approximation." I also ran the numbers, so I know where the answer should be and I wanted to guide you in the right direction. I might suggest doing one more iteration of your calculations. Try 0.55 radians. I think you'll be pleasantly surprised.
anonymous
  • anonymous
difference is ab0ut 5.6 percent.. would it be wrong if we just looked at theta vs. sin theta. rather than sin theta vs. theta /5
Mani_Jha
  • Mani_Jha

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