Maths question doing my head in!

londonman81

I'm trying to solve:

SIN(0.25x) = 0.05 for all x in the range from 0 to 360 degrees.

I get x = 11.46 and 168.54.

But when I plug these values back into the equation, the second one does not work out.....I got the second answer using the fact that SIN X = SIN (180 - X). So why doesn't it work...doing my head in!!

Thanks!

L

dmg24

x = 11.46 is correct, but then to find the next answer you need to do sin (180 - (0.25 * 11.46)), which would make x = 708.54 (though of course this answer would appear within 0 and 360 degrees).

Hope that makes sense, if not, give me a shout! x

londonman81

dmg24 wrote: »

x = 11.46 is correct, but then to find the next answer you need to do sin (180 - (0.25 * 11.46)), which would make x = 708.54 (though of course this answer would appear within 0 and 360 degrees).

Hope that makes sense, if not, give me a shout! x

Surely there is another answer between 0 to 360 since there is another angle which will have a SIN of 0.05. Then we just take a quarter of that to get x don't we?

Alfie_E

No, you have to multiply by four, as dmg24 said.

sin(2.87°) = 0.05
sin(177.13°) = 0.05
sin(362.87°) = 0.05
…

So,

0.25x = 2.87°, 177.13°, ...
x = 11.46°, 708.54°, ...

Or you can look at it as:

If 0° ≤ x < 360°, then 0° ≤ 0.25x < 90°.

dmg24

Yep, Alfie E is spot on! x