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Graphs of Trigonometric Functions

Plot the six different trig functions, discover their illuminating interactions, and ride the wave!

Graphs of Trigonometric Functions Warmup

If the graph in red is \( y = 3\sin(x) \), what could the graph in blue be?

What's the minimum possible value of \( y \) for

\[ y = -5 \sin(2x - \pi) - 2 ? \]

The \( \arccos \) function is typically defined by taking the inverse of a cosine with a domain of \( [0, \pi) \). What would be the effect if the inverse was of a cosine with a domain of \( [0, 2\pi) \) instead? (The graphs below may help.)

Graph of \( f(x) = \cos(x) \):

Graph of \( f(x) = \arccos(x) \):

The interval depicted is 0 to \(4 \pi \). Which of these could not represent the graph above?

Starting from the basic definition of the tangent function, which is these facts most directly implies the tangent graph has a vertical asymptote at \( \frac{\pi}{2} \)?


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