Here are the essential concepts you must grasp in order to answer the question correctly.
Double Angle Formulas
Double angle formulas are trigonometric identities that express trigonometric functions of double angles in terms of single angles. For example, the sine double angle formula states that sin(2x) = 2sin(x)cos(x). Understanding these formulas is crucial for solving equations involving multiple angles, as they allow us to rewrite the equation in a more manageable form.
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Solving Trigonometric Equations
Solving trigonometric equations involves finding the angles that satisfy a given trigonometric equation. This often requires isolating the trigonometric function and using inverse functions or known values of trigonometric ratios. In this case, we need to manipulate the equation to find the values of 'x' that satisfy the equation within the specified 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 we are considering all values from 0 to 2Ο, including 0 but excluding 2Ο. Understanding interval notation is essential for determining the valid solutions to the trigonometric equation, as it restricts the possible values of 'x' to a specific range.
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