Graphs of Trigonometric Functions

Graphs of Trigonometric Functions Warmup


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

What's the minimum possible value of y y for

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

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

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

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

The interval depicted is 0 to 4π4 \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 π2 \frac{\pi}{2} ?


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