Can a Trigonometric Equation Be Solved Algebraically?

[mike133]

Hi,
I wolud like to solve the folowing equation:
A*cos(B*t)+sin(B*t)*(C-t)-D=0 (t is unknown)
It is urgent.
Thanks in advance.
Regards
Mike

 

[Char. Limit]

Unless you have specific numerical values for at least some of the constants A, B, C, and D, this isn't solvable for t. Sorry.

 

[mike133]

Huh... is it possible to make an approxiamtion?

I would like to calculate the intersection between a sine function and a linear function. A sine function is of a form: y=A*sin(x). A linear function intersects sine function in two points. The first one (P1(pi,0)) is known, but we do not know the other one. We know an area between the x-axis and the sine + linear functios (look at the sketch). After integration we get an equation form the first post.
Regards,
Mike

 

[Char. Limit]

Well you have a problem here, then, because a linear function CAN'T intersect a sine function in exactly two points.

 

[mike133]

Yes, they intersect in 3 points, but the third point is not important for me. I am not sure if you can see the sketch, I am sure I attached it, but I cannot see it.

 

[paulfr]

You have not specified the linear equation
So let's take a simple example

y=0.5 intersecting y=sin x
So we have
sin x = 0.5
Take the arcsine of both sides.
x = arcsine 0.5
Which yields pi/6 and 5pi/6 for 0 < x < 2pi

Similar approach should work for any linear equation y = mx + b

Edit in;
Looking at your equation above, you may not be able to solve it
algebraically. You may need to do it numerically.
A graphing calculator will be a big help.
It simply pick hundreds of values for t and calculates what that
gives for the equation and locates where the value is zero.
Just brute force math.