Finding Multiple Angles from Sine Values on the Unit Circle

[Ethan]

Homework Statement

A straight wire 0.280 m in length carries a current of 3.40 A. What are the two angles between the direction of the current and the direction of a uniform 0.0400 T magnetic field for which the magnetic force on the wire has magnitude 0.0250 N?

Relevant Equations

F=ILBsin

I got 41 and correspondingly 49 from this. It said its wrong

 

[Vanadium 50]

Please show your work.

 

[Ethan]

0.025=3.4*.28*.04sinx sin^-1(0.025/0.3808)=41

 

[Vanadium 50]

I have no idea where you got that, but am sure 0.025 does not equal 41.

I recommend that you show your work step by step and only put numbers in at the end.

 

[haruspex]

I have no idea where you got that, but am sure 0.025 does not equal 41.

It was two separate equations.

0.025=3.4*.28*.04sinx
sin^-1(0.025/0.3808)=41

The 0.3808 appears to be a typo for a tenth of that.

 

[Ethan]

 

[TSny]

41^o appears to be correct. But why did you choose the complementary angle (49^o) for the second angle?

sin(41^o) ≠ sin(49^o)

 

[Ethan]

cos^-1(0.6565) is 86.2 but that didn't work. How am I supposed to find a second angle?

 

[haruspex]

cos^-1(0.6565) is 86.2 but that didn't work. How am I supposed to find a second angle?

Draw two straight lines crossing. If one of the angles formed is x, what is the other?
Alternatively, if x=a is one solution of sin(x)=y, what is the other in the range 0 to 360?

 

[TSny]

cos^-1(0.6565) is 86.2 but that didn't work. How am I supposed to find a second angle?

You have shown that sinθ = .6565. So, you need to find two angles θ for which sinθ = .6565

You probably remember that sin(30^o) = 0.5
Can you think of another angle whose sine is 0.5? What is the relation between the two angles?

Try this interactive unit circle. Click on the "Angles" button to display angles on the circle. As you move around on the circle, the length of the green line corresponds to the sine of the angle.