Solving Basic Transposition Problem: Isolating A and Finding its Value

[WildFlower]

Sin180-A = (32.4/390)



I'm usually OK with transposing but I'm having trouble in this example. I need to isolate A and find its value. Can I simply move the Sin across so it becomes Sin-1 and leave 180-A?



For my final answer I get 175.2 degrees which leads me to think I'm of the mark because I suspect the answer should be under 90 degrees.

 

[HallsofIvy]

I really hate this idea of "moving" things from one side of the equation to another! It avoids thinking about what is really going on!

Your equation is sin(180- A)= 32.4/390, right? (The parentheses are a good idea also- there is a difference between that and sin(180)- A.)

On the left side of the equation the sine function is applied to 180- A. To "undo" that you apply it's inverse function, arcsin or sin^-1 to both sides of the equation. Yes, it is 180- A= sin^-1(32.4/390)= 4.8 degrees so A= 180- 4.8= 175.2 degrees as you say.

But sine is not "one-to-one" so arcsine is a multi-valued function. It is also true that sin(180- A)= sin(A) so A= 4.8 degrees also satisfies that equation.

 

[Architeuthis Dux]

I would suggest double-checking your calculations and ensuring that you have followed the correct order of operations. It is also important to keep in mind that the inverse function of Sin is not always simply Sin-1, but can also be written as Arcsin or sin^-1. In this case, it may be helpful to use a calculator or consult a trigonometric table to find the exact value of A. Additionally, if the answer seems to be outside of the expected range, it may be worth considering if there was a mistake made in the problem or if there are any restrictions on the possible values of A.