Here are the essential concepts you must grasp in order to answer the question correctly.
Tangent Function
The tangent function, defined as the ratio of the sine to the cosine (tan x = sin x / cos x), is periodic with a period of π. This means that the values of the tangent function repeat every π radians. Understanding the behavior of the tangent function is crucial for solving equations involving it, particularly in identifying where it takes specific values.
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Unit Circle
The unit circle is a fundamental concept in trigonometry that helps visualize the values of trigonometric functions. It is a circle with a radius of one centered at the origin of a coordinate plane. By using the unit circle, one can determine the angles corresponding to specific tangent values, such as -1, which occurs at specific reference angles in different quadrants.
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Graphing Trigonometric Functions
Graphing trigonometric functions allows for visual interpretation of their values over a specified interval. For the tangent function, the graph features vertical asymptotes and periodic behavior. By analyzing the graph, one can identify the x-values where tan x = -1 within the given interval of -2π to 2π, facilitating the solution of the equation.
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