Can a Trigonometric Equation Be Solved Algebraically?

AI Thread Summary
The equation A*cos(B*t) + sin(B*t)*(C-t) - D = 0 cannot be solved algebraically without specific numerical values for the constants A, B, C, and D. While approximations may be considered, the intersection of a sine function and a linear function typically occurs at three points, not two, which complicates the analysis. A suggested method for finding solutions involves using numerical approaches or graphing calculators to identify where the function equals zero. The discussion emphasizes the limitations of algebraic solutions for such trigonometric equations. Overall, numerical methods are recommended for solving the equation effectively.
mike133
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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
 
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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.
 
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
 
Well you have a problem here, then, because a linear function CAN'T intersect a sine function in exactly two points.
 
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.
 

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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.
 
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