Here are the essential concepts you must grasp in order to answer the question correctly.
Tangent Function
The tangent function, denoted as tan(x), is a fundamental trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle. It can also be expressed as tan(x) = sin(x)/cos(x). Understanding the behavior of the tangent function, including its periodicity and asymptotes, is crucial for solving equations involving it.
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Solutions of Trigonometric Equations
Trigonometric equations often have multiple solutions due to the periodic nature of trigonometric functions. For example, the equation tan(x) = 0 has solutions at specific angles where the tangent function crosses the x-axis. Recognizing that these solutions repeat every π radians is essential for finding all possible solutions.
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Unit Circle
The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is a vital tool in trigonometry for understanding the values of sine, cosine, and tangent at various angles. By analyzing the unit circle, one can easily determine the angles where tan(x) = 0, specifically at integer multiples of π.
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