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Geometry

# Graphs of Trigonometric Functions: Level 2 Challenges

Which of the following could be the function graphed above?

What is the amplitude of the graph of $\Large f(x) = \sin\left(x + \frac{\pi}{3}\right) + \cos\left(x+\frac{\pi}{6}\right)?$

Given the graph above of $$y = \color{red}{A}\sin(x)+\color{blue}{B}\cos(x)$$ for integers $$\color{red}{A}$$ and $$\color{blue}{B},$$ find $$\color{red}{A}-\color{blue}{B}.$$

$\large \color{purple}{g(x)=\cos|x|+\sin|x|}$

Find the fundamental period of the function $$\color{purple}{g(x)}$$.

Find the fundamental period of the function $$f(x) =\sin(36x)$$.

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