Question

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.

Answer 1

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 \(\theta \lt 1\)

Answer 2

umm can u tell me if 0.02 is right?

Answer 3

when i put in the radians i got 0.019

Answer 4

I'm getting something close to 0.5 radians.

Answer 5

the way im doing is i set up it like this sintheta= 0.95(theta)

Answer 6

and my calculator is is in radians

Answer 7

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. \[0.95 \sin \theta = \theta\]

Answer 8

sin (0.5) =0.479 radians
0.5/0.95=0.526

Answer 9

That looks like what I got.

Answer 10

Within 1%

Answer 11

so to get the degree do i just say 0.5 radians (180 degrees)/radians

Answer 12

\[\rm degrees = {180 \over \pi}\]

Answer 13

so its not 0.5 radians time 180 degrees/ radians

Answer 14

is the angle 90

Answer 15

Negative. The conversion is\[\rm degrees = {180 \over \pi}\]

You should get approximately 28.5.

Answer 16

how canu please show me

Answer 17

Sorry. \[\rm degress = [radians] {180 \over \pi}\]

Answer 18

so 0.5 is not treated as radians because i thought it was 0.5pi(180/pi)

Answer 19

the question asks the difference betwene theta and sin theta should only be 5 percent but in my situation ios only 1

Answer 20

I think I'm confused as to where you are confused.

We solved for theta such that a 5% difference had to be satisfied.

Answer 21

okay just to make sure i calculated properly i did o.526-0.479=0.47x100 =5percent

Answer 22

so the difference is 5 percent

Answer 23

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 )

Answer 24

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.

Answer 25

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

Answer 26

http://openstudy.com/users/anna818#/updates/4f68107de4b0f81dfbb53ce7
I did it that way.....