Math Problem Statement

a. Find the period of f(x) b. Graph one cycle of f(x) on the axes below and clearly label the asymptotes, and at least three points on the curve. Simplify: cos(x + π/6) + sin(x - π/3)

Solution

Let’s solve the questions step by step.

4a. Find the period of f(x)=3tan(2x)f(x) = -3\tan(2x):

For a general tangent function, the period is calculated as:

Period=πb\text{Period} = \frac{\pi}{|b|}

where bb is the coefficient of xx inside the tangent function. In this case, b=2b = 2. Thus:

Period=π2\text{Period} = \frac{\pi}{2}

The period of f(x)f(x) is π2\frac{\pi}{2}.


4b. **Graph one cycle of ( f(x) = -3\t

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Periodic Functions
Simplification of Trigonometric Expressions

Formulas

Period of tangent function: Period = π / |b|
Trigonometric addition formulas

Theorems

Basic properties of tangent functions
Trigonometric identities

Suitable Grade Level

Grades 10-12