Solving a problem using a formula for arcs of contact

[Probability]

I am not sure what to do with the pi - 2sin^-1 in this formula.

Pi - 2sin^-1 (500 - 355) / (2 x 1500)

The answer is 3.045 rad

any help much appreciated

 

[Ishuda]

I am not sure what to do with the pi - 2sin^-1 in this formula.

Pi - 2sin^-1 (500 - 355) / (2 x 1500)

The answer is 3.045 rad

any help much appreciated

I assume the probem is
\(\displaystyle \pi - 2 \arcsin(\frac{500\space -\space 355}{2\space *\space 1500})\)

Just compute the arcsin and subtract twice that from the value of \(\displaystyle \pi\).

 

[Probability]

I assume the probem is
\(\displaystyle \pi - 2 \arcsin(\frac{500\space -\space 355}{2\space *\space 1500})\)

Just compute the arcsin and subtract twice that from the value of \(\displaystyle \pi\).

I have tried that I think but keep getting an error sign because arcsin does not like negative numbers

 

[Ishuda]

I have tried that I think but keep getting an error sign because arcsin does not like negative numbers

What negative number? You have
\(\displaystyle \arcsin(\frac{500\space -\space 355}{2\space *\space 1500})\)

arcsin should do negative numbers but it won't do numbers greater than one in magnitude.

 

[Probability]

What negative number? You have
\(\displaystyle \arcsin(\frac{500\space -\space 355}{2\space *\space 1500})\)

arcsin should do negative numbers but it won't do numbers greater than one in magnitude.

Sorry I think you have misread my post?

\(\displaystyle -2arcsin(\frac{500\space -\space 355}{2\space*\space1500})\)

 

[Probability]

Any reason for showing 500-355 instead of 145, and 2*1500 instead of 3000 ?

Yes but I did not go into depth to fully explain the context of the workings. The reason for the 500 - 335 is because this is a belt type problem and the belt operates round a number of degrees of each pulley. The smaller pulley is turning at 1500 RPM and I take the 2 to be used for average?

I seem to have found a way to work out the answer 3.045 rads this way;

Pi - 2 arcsin (500 - 335) / (2 x 1500)

The brackets work out as 0.04835172 using full calculator accuracy. Multiply this by 2 and then take the arcsin of the number which is 0.096855707, then press the + - key and add Pi = 3.045 rads as the answer shows.

The only question I have remaining is am I working this problem out my own way and not the correct mathematical way that I don't know?

 

[Ishuda]

Sorry I think you have misread my post?

\(\displaystyle -2arcsin(\frac{500\space -\space 355}{2\space*\space1500})\)

I was talking about the arcsin part.
\(\displaystyle \frac{500\space -\space 355}{2\space*\space1500}\) ~ 0.0483333333333333

\(\displaystyle arcsin(0.0483333333333333)\) ~ 0.0483521718168557

2 * 0.0483521718168557 ~ 0.0967043436337114

\(\displaystyle \pi\space -\space 0.0967043436337114\) ~ 3.04488830995608 ~ 3.045

 

[Probability]

I was talking about the arcsin part.
\(\displaystyle \frac{500\space -\space 355}{2\space*\space1500}\) ~ 0.0483333333333333

\(\displaystyle arcsin(0.0483333333333333)\) ~ 0.0483521718168557

2 * 0.0483521718168557 ~ 0.0967043436337114

\(\displaystyle \pi\space -\space 0.0967043436337114\) ~ 3.04488830995608 ~ 3.045

Sorry I must have misunderstood