Here are the essential concepts you must grasp in order to answer the question correctly.
Trigonometric Functions
Trigonometric functions, such as sine, cosine, and tangent, relate angles to the ratios of sides in right triangles. In this question, the cosine function is central, as the equation involves cosΒ² x and cos x. Understanding how these functions behave and their values on the unit circle is essential for solving trigonometric equations.
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Quadratic Equations
The equation cosΒ² x - cos x - 1 = 0 is a quadratic equation in terms of cos x. Quadratic equations can be solved using various methods, including factoring, completing the square, or the quadratic formula. Recognizing the structure of the equation allows for the application of these methods to find the values of cos x.
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Interval Notation
The interval [0, 2Ο) specifies the range of values for x in which we are interested in finding solutions. This notation indicates that x can take any value from 0 to 2Ο, including 0 but excluding 2Ο. Understanding interval notation is crucial for determining the valid solutions of the trigonometric equation within the specified range.
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