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johann1301
- 217
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Homework Statement
solve sin x - 2x = 0
The Attempt at a Solution
I can see that zero is a solution, but i don't know how to actually solve it in a general way. Can somebody give me a hint?
johann1301 said:Use the second method that "Char. Limit" proposed. Or perhaps you know another way? I sure dont...
The first step in solving this equation is to isolate the sin x term by adding 2x to both sides of the equation, resulting in sin x = 2x.
To solve for x in this type of equation, you can use a graphing calculator or a table of values to find the intersections between sin x and 2x. This will give you approximate values for x, which can then be refined using algebraic techniques.
Yes, this equation can have multiple solutions. Since the sine function is periodic, there are infinitely many values of x that satisfy the equation sin x = 2x. However, when solving for x, we typically only consider solutions within a specific interval, such as 0 to 2π.
Yes, there are several techniques for solving these types of equations, such as using the unit circle, trigonometric identities, and inverse trigonometric functions. It is important to have a good understanding of these concepts when working with trigonometric equations.
No, this equation cannot be solved algebraically. Because of the periodic nature of the sine function, it is not possible to isolate x on one side of the equation using algebraic techniques. Instead, we must use a combination of algebra and trigonometry to find approximate solutions.