Math help needed (night before a big test); A.K.A 'ATTENTION MATH FREAKS!'

[Mass_Liberal]

Question:

Edit: math talk doesn't work on DU so w/ words

Find the number x to two significant digits if 0 is less than or equal to x which is less than equal to (pi/2) and if sin x= .6669


Note: Evaluate without using a table or calculator.

[katinmn]

1. Don't look at me. I'm re-learning 7th grade math

(my daughter's)

[OldLeftieLawyer]

2. Listen,

go to law school.

[Mass_Liberal]

3. I'm in high school

Believe me, if it were up to me, I'd do 6 months hard labor to drop math forever.

[smartvoter]

4. LOL!!! nt

[Kellanved]

5. calculator allowed?

If so: just arcsin(.6669)

[Mass_Liberal]

7. nah

the bastards won't let me use the calculator.

[Mass_Liberal]

6. kick

this is urgent!

[Crazy Guggenheim]

8. Hmmm.

[skygazer]

9. Ummmm.......

Hemingway? :dunce:

[dbonds]

10. In degrees or Radians

The first part 0 LTorE to x LTorE PI/2 shows that x is an angle in the 1st quadrant. you then just need to take the arcsin of .6669 which is 42 degrees (to 2 sig digits) or .73 radians

[Mass_Liberal]

11. ok

I know that the first part narrows it down to the 1st quadrant. But how do I do inverse of sin(.6669) without a calculator?

[Crazy Guggenheim]

13. Use the definition the sin. y/r. Where r = Hypotenuse.

[dbonds]

14. That is much harder.

Do you not have tables where you can see and interpelate the values? If not you will need some aproximation formula. Did they give you any of those. I don't remember any. I know there are a lot of transformation formula too, but they would depend on you having tables.

[dbonds]

21. I have done a google for different arcsin

identity functions. I can not find one without having 1 more piece of info (like the cos(x) ) Are you supposed to have memorized values for PI/4 and PI/6? - you could use that to interpelate.

[Mass_Liberal]

12. bump

or I'm screwed :(

[Crazy Guggenheim]

15. Can you assume r=1?

[Crazy Guggenheim]

16. I just thought of something.

Can it be assume you are using x as the horizontal?

[Telly Savalas]

17. What class is this for?

My trig is really shaky, so my first reaction would be to use a numerical method, in particular the Taylor series expansion for the arcsin function. If this isn't a Calc II class or so, then I don't think you'd be expected to know that, and even if you were it's an awful lot of multiplying and dividing by hand.

[Crazy Guggenheim]

18. And don't forget Eliptical Appoximations either ........

:rofl:

[Telly Savalas]

22. Ya got a better concrete solution?

Post #20 agrees that it's a way of breaking the problem down into arithmetic that can be done by hand (albeit painfully).

[Crazy Guggenheim]

23. It's got to be simpler than that.

[Telly Savalas]

27. That's why I asked what course it was.

If it's a Calc II course, they're probably expecting you to use the Taylor Series apporach I suggested. (And it's not like a Taylor series are that sophisticated.) If however it's in a course that doesn't assume knowledge of calculus, then obviously a different solution is in order. But since nobody else here can think of an alternate method of computing arcsins by hand, I don't see what's so laughable about using Taylor series.

[illini]

19. Math, algebra, calculus are for people who likemath, algebra, calculus.

Ick I hate that stuff.

[Bill McBlueState]

20. here's your answer

Go to http://mathworld.wolfram.com/InverseSine.html and scroll down to "The Maclaurin series for the inverse sine..."

You'll still have to crunch some numbers, but it turns the problem into simple multiplications and additions.

[Crazy Guggenheim]

24. How's it going?

[Crazy Guggenheim]

25. Anything yet?

[BrewerJohn]

26. Here's a solution that takes less calculation than using series

If you play with the numbers a little bit, it becomes clear that x is just a hair less than pi/4 (recall that sin(pi/4) = 0.707 (half the square root of 2)). So if you use the trig identity

sin(a-b) = sin a cos b - cos a sin b

with a set equal to pi/4, you get

0.6669 = sin(pi/4 - b) = sin(pi/4)cos b - cos(pi/4)sin b.

But both sin(pi/4) and cos(pi/4) are equal to 0.707, so immediately this reduces to

0.6669 = 0.707(cos b - sin b), which you solve for b. But b is pretty dang small, so you can use the simplest approximation for both functions: cos b is approximately 1, and sin b is approximately b, for b much smaller than 1. So then

0.6669 = 0.707(1 - b) (approximately). Solve this and get b = 0.0567 (approximately), after some arithmetic. Then the total angle x is pi/4 - 0.0567, or 0.73 to two places.

[Crazy Guggenheim]

28. That's one of 'em!!