Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Trigonometric Functions
Inverse trigonometric functions, such as cos⁻¹ (arccosine), are used to find the angle whose cosine is a given value. In this context, cos⁻¹(x/4) represents the angle whose cosine equals x/4. Understanding how to manipulate these functions is essential for solving equations involving them.
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Solving Trigonometric Equations
Solving trigonometric equations involves isolating the variable and finding all possible angles that satisfy the equation. In this case, the equation includes a coefficient (4/3) and a constant (π), which requires careful algebraic manipulation to isolate x and determine its exact values.
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Understanding Radian Measure
Radian measure is a way of measuring angles based on the radius of a circle. In this problem, π radians corresponds to 180 degrees. Recognizing the relationship between radians and degrees is crucial for interpreting the solutions correctly and ensuring they fall within the appropriate range for the cosine function.
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