Satisfying trig equations between (0,2pi)

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SUMMARY

The discussion centers on solving the trigonometric equation cos2x - cos x - 1 = 0. Participants identify that this equation can be treated as a quadratic in terms of cos x, analogous to solving x2 - x - 1 = 0. The solution involves applying the quadratic formula to find the values of cos x, which can then be used to determine the angles x within the interval (0, 2π).

PREREQUISITES
  • Understanding of trigonometric identities involving cosine
  • Familiarity with quadratic equations and the quadratic formula
  • Knowledge of the unit circle and angle measurement in radians
  • Ability to manipulate algebraic expressions
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  • Study the quadratic formula and its application in solving equations
  • Learn how to derive and apply trigonometric identities
  • Explore the unit circle for determining angles corresponding to cosine values
  • Practice solving various trigonometric equations within specified intervals
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Students studying trigonometry, educators teaching trigonometric equations, and anyone looking to enhance their problem-solving skills in mathematics.

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Homework Statement


cos^2 x-cos x- 1= 0


Homework Equations


several trig identities involving cos


The Attempt at a Solution


i tried applying identites everywhere, no luck. I've tried using it as a trinomial...no luck...and I've tried adding one to both sides and still no luck...please help lol
 
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banfill_89 said:

Homework Statement


cos^2 x-cos x- 1= 0


Homework Equations


several trig identities involving cos


The Attempt at a Solution


i tried applying identites everywhere, no luck. I've tried using it as a trinomial...no luck...and I've tried adding one to both sides and still no luck...please help lol

If you squint your eyes a bit, you might notice that this is a quadratic in cos x. Think about how you would solve x^2 - x - 1 = 0, but keep in mind that you're solving for the cosine of x, not x.
 

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