Question

solve trig equation: sin (x/2) = -√2/2
(-2pie to 2pie)
Answer: x/2= -pie/4, -3pie/4, 5pie/4, 7pie/4
I don't understand why angles are listed twice such as -pie/4 and 7pie/4 Isn't that the same???

Answer 1

yes.. but your domain requires that...
so, they are equivalent is analysis but technically, thwey mean different
-pi/4 => go pi/4 clockwise
7pi/4=> go 7pi/4 counter clockwise..

you see, if you are travelling on a unit circle by foot, you'd take more time and spend more energy in the latter than the former.

Answer 2

so, the directions do matter.

Answer 3

so from -pi/4 to 2pi you cover 3/4 of the circle but from 7pi/4 to 2pi you cover 1-1/4 of the circle

Answer 4

no
7pi/4-> covers 7/8th of a circle
-pi/4-> covers 1/8th of a circle

Answer 5

but in opposite directions...
the final position vectors are the same....

This topic leads to many important conclusions used in Thermodynamics, vector calculus, etc

Answer 6

ok i get it: if it is positive you move clockwise, if negative you move counterclockwise. Can I just ask you when it says: sin (theta/2) = -√2/2. How would you describe this problem in words?

Answer 7

no.. +ve->counterclock
-ve->clockwise

Answer 8

what do you mean in words?

Answer 9

When I see a problem like that on the test I don't know what I need to solve, so i would like to translate it into words