How Do You Solve the Equation 4 Sin x + 2 Cos x = 3 on the Interval [0, 2 Pi]?

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To solve the equation 4 sin x + 2 cos x = 3 on the interval [0, 2π], one can use trigonometric identities and algebraic manipulation. The equation can be rewritten in terms of a single trigonometric function by expressing it in the form R sin(x + φ), where R is the amplitude and φ is the phase shift. This approach simplifies finding the values of x that satisfy the equation within the specified interval. The discussion highlights the importance of understanding trigonometric identities for solving such equations. Ultimately, the original poster successfully solved the equation independently.
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Hi, i signed up for a math exam in Norway come may, and i have to educate myself, because there are no lessons involved, only an exam, but here goes;

Its basic, you have an equation; 4 sin x + 2 cos x = 3 x range is [0, 2 pi]

I guess this is basic stuff, so don't laugh, i couldn't find any examples of this kinda equation in my textbooks, and when i found it in an exam preview i got kinda stressed. I tried to apply some of the different rules of pytagoran identities and such, but with no success.

A friend of mine used this forum for his ib studies, and said that most ppl here rock at math and were really friendly as well, so please help me out :)
 
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well, never mind, i solved it myself!
 
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