Find x sin^n (x) - cos^n (x) = 0

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Start date Mar 24, 2005

In summary, the general solution to the equation "Find x sin^n (x) - cos^n (x) = 0" is that x can take on any value that satisfies the equation, including 0, π, 2π, -π, -2π, and any other multiple of π. The equation can have infinite solutions as the values of sine and cosine are cyclical and repeat every 2π radians. It is also possible for the equation to have no solutions if the powers of sine and cosine cancel each other out. To solve the equation, algebraic methods such as factoring, substitution, or the quadratic formula can be used, as well as a graphing calculator to find the points of intersection between the

Mar 24, 2005

no name

sin^n (x) - cos^n (x) = 0

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Mar 24, 2005

Edgardo

Is it Pi/4 ?

Mar 24, 2005

dextercioby

Science Advisor

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It admits an infinity of solutions,because it's simple to see that among the solutions of the initial equation,there can be found the solutions to:
tan x=1 ,x=pi/4+k*pi,k in Z

Daniel.

1. What is the general solution to the equation "Find x sin^n (x) - cos^n (x) = 0"?

The general solution to this equation is that x can equal any value that makes the statement true. This includes values such as 0, π, 2π, -π, -2π, and any other multiple of π.

2. Can the equation "Find x sin^n (x) - cos^n (x) = 0" have infinite solutions?

Yes, the equation can have infinite solutions as x can take on any value that satisfies the equation. This is because the values of sine and cosine are cyclical and repeat every 2π radians.

3. Is it possible for the equation "Find x sin^n (x) - cos^n (x) = 0" to have no solutions?

Yes, it is possible for the equation to have no solutions. This can occur if the powers of sine and cosine cancel each other out, leaving a constant value on one side of the equation.

4. How do you solve the equation "Find x sin^n (x) - cos^n (x) = 0"?

To solve this equation, you can use algebraic methods such as factoring, substitution, or the quadratic formula. You can also use a graphing calculator to find the points where the curve of sin^n (x) and cos^n (x) intersect, which will give you the solutions for x.

5. What is the significance of the equation "Find x sin^n (x) - cos^n (x) = 0" in mathematics?

This equation is significant in mathematics as it involves the trigonometric functions sine and cosine, which have many real-world applications. Solving this equation can also help in understanding the relationships between different trigonometric functions and their powers.