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. Key identities include the Pythagorean identity, angle sum and difference identities, and double angle formulas. In this problem, recognizing that sin(2x) can be expressed using the double angle identity sin(2x) = 2sin(x)cos(x) is crucial for simplifying the equation.
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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, we need to manipulate the equation to express it in terms of a single trigonometric function, allowing us to find the values of x that satisfy the equation within the interval [0, 2Ο).
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Interval Notation
Interval notation is a mathematical notation used to represent a range of values. The interval [0, 2Ο) indicates that the solutions must be greater than or equal to 0 and less than 2Ο. Understanding this notation is essential for determining the valid solutions to the equation, as it restricts the possible values of x to a specific range, which is important for trigonometric functions that are periodic.
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