Here are the essential concepts you must grasp in order to answer the question correctly.
Trigonometric Identities
Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. In this problem, recognizing that the equation can be rearranged using identities will help simplify the process of solving for x. Key identities include the Pythagorean identity, reciprocal identities, and co-function identities, which are essential for manipulating trigonometric equations.
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Solving Trigonometric Equations
Solving trigonometric equations involves finding the angles that satisfy the equation within a specified interval. This often requires isolating the trigonometric function and using inverse functions or identities to find solutions. In this case, rearranging the equation to isolate cos x will allow us to determine the values of x that meet the criteria of the problem.
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Interval Notation
Interval notation is a mathematical notation used to represent a range of values. In this problem, the interval [0, 2Ο) indicates that we are looking for solutions within one full rotation of the unit circle, starting from 0 and going up to, but not including, 2Ο. Understanding this notation is crucial for determining the valid solutions for x in the context of trigonometric functions.
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