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Graphing Trigonometric Functions>
Graphing Trigonometric Functions 3Graphing Trigonometric Functions 3
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Question 1 of 4
1. Question
Graph the trigonometric function within the domain `-pi/4≤x≤pi/4``y=2tan 4x`Hint
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Period Fomula
$$P_{\text{tan}}=\frac{\pi}{\color{#00880A}{b}}$$First, solve for the period of the function`b` `=` `4` $$P_{\text{tan}}$$ `=` $$\frac{\pi}{\color{#00880A}{b}}$$ `=` $$\frac{\pi}{\color{#00880A}{4}}$$ Substitute known values Asymptotes will occur within the domain for the values of `tan` that are undefined`\text(tan) -pi/8` `=` `\text(undefined)` `\text(tan) pi/8` `=` `\text(undefined)` 
To graph the `tan` curve, start at x-axis of the lower domain `(-pi/4)` and draw a curve heading up to the first asymptote `(-pi/8)`. This will cover half of a period of the curve.Repeat the process until you reach the x-axis of the upper domain `(pi/4)`, which will also show half of the curve.First curve
Second curve
Third curve
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Question 2 of 4
2. Question
Graph the trigonometric function within the domain `-pi/2≤x≤2pi``y=cot x`Hint
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Period Fomula
$$P_{\text{cot}}=\frac{\pi}{\color{#00880A}{b}}$$First, solve for the period of the function`b` `=` `1` $$P_{\text{tan}}$$ `=` $$\frac{\pi}{\color{#00880A}{b}}$$ `=` $$\frac{\pi}{\color{#00880A}{1}}$$ Substitute known values `=` `pi` Recall that `\text(cot)=1/(\text(tan))`Asymptotes will occur within the domain for the values of `cot` that are undefined or when the value of `tan` is `0``\text(cot) 0` `=` `\text(undefined)` `\text(cot) pi` `=` `\text(undefined)` `\text(cot) 2pi` `=` `\text(undefined)` 
To graph the `cot` curve, start at x-axis of the lower domain `(-pi/2)` and draw a curve and heading down to the first asymptote at the y-axis. This will cover half of a period of the curve.Repeat the process until you reach the x-axis of the upper domain `(2pi)`First curve
Second curve
Third curve
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Question 3 of 4
3. Question
Graph the trigonometric function within the domain `-1≤x≤1``y=cot pix`Hint
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Period Fomula
$$P_{\text{cot}}=\frac{\pi}{\color{#00880A}{b}}$$First, solve for the period of the function`b` `=` `pi` $$P_{\text{tan}}$$ `=` $$\frac{\pi}{\color{#00880A}{b}}$$ `=` $$\frac{\pi}{\color{#00880A}{pi}}$$ Substitute known values `=` `1` Recall that `\text(cot)=1/(\text(tan))`Asymptotes will occur within the domain for the values of `cot` that are undefined or when the value of `tan` is `0``\text(cot) -1` `=` `\text(undefined)` `\text(cot) 0` `=` `\text(undefined)` `\text(cot) 1` `=` `\text(undefined)` 
To graph the `cot` curve, start at the lower domain `(-1)` and draw a curve heading down to the first asymptote at the y-axis. This will cover a period of the curve.Repeat the process until you reach the x-axis of the upper domain `(1)`First curve
Second curve
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Question 4 of 4
4. Question
Graph the trigonometric function`y=sin(x+pi/4)`Hint
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General Form of a Sin Function with Horizontal Shift
`y=``a` `\text(sin)` `b``(x-``h``)`Period Fomula
$$P=\frac{2\pi}{\color{#00880A}{b}}$$First, identify the values of the function`y` `=` `a` `\text(sin)` `b``(x-``h``)` `y` `=` $$\color{#004ec4}{1}\;\text{sin}\;\color{#00880A}{1}(x+\color{#9a00c7}{\frac{\pi}{4}})$$ `a` `=` `1` `b` `=` `1` `h` `=` `pi/4` Next, solve for the period of the function$$P$$ `=` $$\frac{2\pi}{\color{#00880A}{b}}$$ `=` $$\frac{2\pi}{\color{#00880A}{1}}$$ Substitute known values `=` `2pi` To graph the `sin` curve, it is better to divide the value of its period into for parts and have the curve meet the following conditionsCurve starts at `(0,0)`
Curve reaches peak of amplitude (`a`) at 1st quarter
Curve intercepts x-axis at 2nd quarter
Curve reaches minimum amplitude at 3rd quarter
Curve starts at x-axis again at the period (`P=4pi`)
This will be the sin curve for `y=\text(sin) x+pi/4` with a period of `2pi`Shift the graph horizontally `h=pi/4` units to the left. Since the labels are in intervals of `pi/4`, we move the graph `1` label to the left
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