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Saitama
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Homework Statement
If sin x + sin2x + sin3x= 1, then find out the value of cos6x-4cos4x+8cos2x.
Homework Equations
The Attempt at a Solution
How should i start?
I don't find any way to convert them to cos 6x or cos 4x.
SammyS said:Try using [itex]\displaystyle \sin \theta + \sin \varphi = 2 \sin\left( \frac{\theta + \varphi}{2} \right) \cos\left( \frac{\theta - \varphi}{2} \right)[/itex] to combine sin(x) + sin(3x) .
-- Just a possibility.
eumyang said:I don't think the problem was copied correctly. I've seen this problem before. The numbers in front of the x's are supposed to be exponents, not multiples of angles.
The problem should be as follows:
If
[itex]\sin x + \sin^2 x + \sin^3 x = 1[/itex],
then find out the value of
[itex]\cos^6 x - 4\cos^4 x + 8\cos^2 x[/itex].
Here's a hint, and hopefully, it's not a big one:
Rewrite as
[itex]\sin x + \sin^3 x = \cos^2 x[/itex].
Then square both sides and use the identity
[itex]\sin^2 x =1 - \cos^2 x[/itex].
You should eventually get the answer.
Mods: if this is too big of a hint, then please delete.
A sin equation is an equation that involves trigonometric functions, specifically the sine function. It is used to represent relationships between angles and sides in a right triangle.
To solve a sin equation, you can use trigonometric identities and properties to manipulate the equation and isolate the variable. You can also use a calculator or tables to find the values of sine for specific angles.
The purpose of solving a sin equation is to find the value of the variable in the equation, which can be used to solve real-world problems involving triangles and angles. It is also used in various fields such as engineering, physics, and astronomy.
To find the value of cos6x-4cos4x+8cos2x, you can use the trigonometric identities cos(2x) = 2cos^2(x) - 1 and cos(3x) = 4cos^3(x) - 3cos(x). By substituting these identities and simplifying the equation, you can find the value of the expression.
Yes, you can use the unit circle to solve a sin equation by plotting the angle on the unit circle and using the coordinates of the point where the angle intersects the circle. The y-coordinate of the point represents the value of sine for that angle. You can also use the Pythagorean theorem to find the value of the opposite or adjacent side of the triangle, which can be used to solve the equation.