Unit 6, Lesson 13
Some New Ratios
Integrated Math 3
Practice
Problem 1
Match each function with its graph.
- \(y=\cot{(\theta)}\)
- \(y=\sec{(\theta)}\)
\(y=\csc{(\theta)}\)
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\(y=\csc{(\theta)}\)
Graph \(y=\cos{(\theta)}\) and \(y=\sec{(\theta)}\) on the same set of axes.
Graph \(y=\tan{(\theta)}\) and \(y=\cot{(\theta)}\) on the same set of axes.
Here is a graph of \(y = \cos(\theta)\) for values of \(\theta\) between 0 and \(\pi\).
A graph. Horizontal axis, theta, scale 0 to 6 pi, by pi. Vertical axis, y, from negative 1 to 1, by 1s. A curve begins at 0 comma 1, crossing the x-axis at pi over 2 and ending at the point pi comma negative 1.
Here is a graph of \(y = \tan(\theta)\).
A graph. Horizontal axis, theta, negative pi over 2 to pi over 2, by pi over 4. Vertical axis, y, negative 3 to 3, by 1s. A curve begins in the bottom left of the graph and curves up, through the points negative pi over 4 comma negative 1, 0 comma 0, and pi over 4 comma 1.
Each of the graphs have been transformed from the original function \(y=\frac1x\). Match each graph with the transformation that was applied.