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Reed College Department of Mathematics & Statistics

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Worksheet Tangent, Cotangent, Secant, and Cosecant

3.

Use the trigonometric function \(f(x) = 4\cot\left(x+\displaystyle\frac{\pi}{2}\right)-1\) to answer the following questions.
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Identify the stretching factor of \(f(x)\)
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State the period of \(f(x)\)
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What is the range of \(f(x)\text{?}\) Enter the range in interval notation.
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The phase shift of \(f(x)\) is units
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The vertical shift of \(f(x)\) is units
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Answer 1.
\(4\)
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Answer 2.
\(3.14159\)
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Answer 3.
\(\left(-\infty ,\infty \right)\)
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Answer 4.
\(\frac{\pi }{2}\)
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Answer 5.
\(\text{left}\)
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Answer 6.
\(1\)
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Answer 7.
\(\text{down}\)
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8.

Use the trigonometric function \(h(x) = 4\csc\left(\displaystyle\frac{\pi}{4}x+\pi\right)\) to answer the following questions.
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What is the period of \(h(x)\text{?}\)
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The phase shift of \(h(x)\) is units
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If the video does not work, click here to watch on YouTube.
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Answer 1.
\(8\)
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Answer 2.
\(4\)
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Answer 3.
\(\text{left}\)
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11.

Use the trigonometric function \(f(x) = 5\tan(4x-5)\) to answer the following questions.
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What is the stretching factor of \(f(x)\text{?}\)
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What is the period of \(f(x)\text{?}\)
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What is the range of \(f(x)\text{?}\) Enter the range in interval notation.
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The phase shift of \(f(x)\) is units
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Answer 1.
\(5\)
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Answer 2.
\(0.785398\)
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Answer 3.
\(\left(-\infty ,\infty \right)\)
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Answer 4.
\(1.25\)
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Answer 5.
\(\text{right}\)
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12.

Determine which equation can be used to find the asymptotes for the following graph.
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Which equation can be used to find the asymptotes for the graph?
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  1. `x=-frac{pi}{8}k`, for any `k` integer.
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  2. `x=frac{3pi}{8} + frac{pi}{2}k`, for any `k` integer.
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  3. `y=frac{pi}{8} + 2pik`, for any `k` integer.
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  4. `y=frac{pi}{4} + frac{pi}{2}k`, for any `k` integer.
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  5. `x=-frac{3pi}{8} + pik`, for any `k` integer.
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Answer.
\(\text{B}\)
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13.

Determine which equation can be used to find the asymptotes for the following graph.
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Which equation can be used to find the asymptotes for the graph?
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  1. `x=frac{pi}{6}k`, for any `k` integer.
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  2. `y=frac{pi}{2}k`, for any `k` integer.
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  3. `x=frac{pi}{4} pm frac{pi}{2}k`, for any `k` integer.
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  4. `y=frac{pi}{4} pm frac{pi}{2}k`, for any `k` integer.
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  5. `x=frac{pi}{2}k`, for any `k` integer.
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Answer.
\(\text{E}\)
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