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

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SUMMARY

The equation 4 sin x + 2 cos x = 3 can be solved on the interval [0, 2π] using trigonometric identities and algebraic manipulation. The solution involves isolating one of the trigonometric functions and applying the Pythagorean identity. The user successfully solved the equation independently after initial struggles, demonstrating the importance of practice and resourcefulness in mathematical problem-solving.

PREREQUISITES
  • Understanding of basic trigonometric functions (sine and cosine)
  • Familiarity with trigonometric identities, particularly the Pythagorean identity
  • Algebraic manipulation skills for solving equations
  • Knowledge of the unit circle and angle measurements in radians
NEXT STEPS
  • Study the application of trigonometric identities in solving equations
  • Practice solving similar trigonometric equations on specified intervals
  • Learn about the unit circle and its role in trigonometric functions
  • Explore graphical methods for solving trigonometric equations
USEFUL FOR

Students preparing for math exams, particularly those focusing on trigonometry, as well as educators seeking to enhance their teaching methods in solving trigonometric equations.

Nadime
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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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