Geometry
Graphs of Trigonometric Functions
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 \( \frac{\pi}{2} \)?