Math Problem Statement

After completing one revolution starting from the initial line, point A is observed to have coordinates (-\frac{ \sqrt{3} }{2} , \frac{1}{2}) on the unit circle. Using that information, please answer the following questions:

Calculate all 6 values of the trigonometric functions (clearly state the formulae used to calculate these functions).

Solution

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Unit Circle
Trigonometric Functions

Formulas

Sine function: \( \sin(\theta) = y \)
Cosine function: \( \cos(\theta) = x \)
Tangent function: \( \tan(\theta) = \frac{y}{x} \)
Cosecant function: \( \csc(\theta) = \frac{1}{y} \)
Secant function: \( \sec(\theta) = \frac{1}{x} \)
Cotangent function: \( \cot(\theta) = \frac{x}{y} \)

Theorems

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Suitable Grade Level

Advanced High School