A bit of mathamatics

[kunalw]

Is there any method to go for solving equations below<br>except for using sin[square]a + cos[square]a = 1<br>any short tricky method<br>6.58*cos(a) = 3.81 + .058*B<br>6.58sin(a) = .0056*B<br>where a is angle in degree B is a numeric value<br>In early need of answer<br>thanking you<br>

 

[Nigel]

Sounds like a college question to me!&nbsp;&nbsp;If so, I think&nbsp;&nbsp;that you need to think about it a little longer! <p>Nigel Waterhouse<br><a href=mailto:n_a_waterhouse@hotmail.com>n_a_waterhouse@hotmail.com</a><br><a href= > </a><br>A licensed aircraft mechanic and graduate engineer. Attended university in England and graduated in 1996. Currenty,living in British Columbia,Canada, working as a design engineer responsible for aircraft mods and STC's.

 

[ambertec]

Since you have two equations in two unknowns, the solution to the problem can be derived. As they say though, &quot;All roads lead to Rome.&quot; There will be no magic solution or special trick to get you to the answer more quickly than the method of solution you allude to.<br><br>Good luck.

 

[ib50]

I agree with the &quot;no magic&quot; way. It looks the best way to use sin^2+cos^2=1. This leaves you with an equation with only B unknown.

 

[navam]

I agree with the last two responses.&nbsp;&nbsp;There are 2 unknowns - a and B - and two equations.&nbsp;&nbsp;If you don't use the known relationship between cos and sin, then it becomes 3 unknowns, cos(a), sin(a) and B and three unknowns can't be solved from 2 equations.&nbsp;&nbsp;So you have to use the relationship between cos(a) and sin(a) which you have stated.

 

[jbartos]

There are a few ways to attack this problem:<br>a. Pencil and paper with some numerical method for the solution of a system of nonlinear transcendental equations. Modern software often use iteration methods since the computer hardware processes them easily.<br>b. Graphical methods are good but not much accurate. Incidentally, what kind of accuracy do you need for that solution?<br>c. The easiest way nowadays is the computer math software. I suggest that you type at your search engine &quot;math software&quot; and some reasonably good packages will appear on the screen. This is what I did long time ago when such packages were inexpensive.<br>d. I used that software and I got the following results:<br>a=0.04058 in radians<br>b=47.66524 in per unit<br>in the interval a&lt;=3 radians and b&gt;0 in per unit