Topics
>
Precalculus>
Trigonometric Functions>
Graph Trigonometric Functions>
Graph Trigonometric Functions 2Graph Trigonometric Functions 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
 1
 2
 3
 4
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
 1
 2
 3
 4
 Answered
 Review

Question 1 of 4
1. Question
Which graph best represents both of the trigonometric functions below?`color(red)(y=cosx)``y=secx`Hint
Help VideoCorrect
Fantastic!
Incorrect
General Form of a Cos Function
`y=``a` `\text(sin)` `b``x`Period Fomula
$$P_{\text{sin}}=\frac{2\pi}{\color{#00880A}{b}}$$First, identify the values of the `cos` function`y` `=` `a` `\text(cos)` `b``x` `y` `=` $$\color{#004ec4}{a}\;\text{cos}\;x$$ `a` `=` `1` `b` `=` `1` Next, solve for the period of the `cos` function$$P_{\text{cos}}$$ `=` $$\frac{2\pi}{\color{#00880A}{b}}$$ `=` $$\frac{2\pi}{\color{#00880A}{1}}$$ Substitute known values `=` `2pi` To graph the `cos` curve, it is better to divide the value of its period into for parts and have the curve meet the following conditionsCurve starts at the peak of the amplitude `(a)`Curve intercepts xaxis at 1st quarterCurve reaches minimum amplitude at 2nd quarterCurve intercepts xaxis again at 3rd quarterCurve starts again at the period (`P=2pi`)Therefore, this will be the `cos` curve for `y=\text(sin) x` with a period of `2pi`Next, recall that `\text(sec) x=1/(\text(cos) x)`Given this, we can graph `y=\text(csc) x` with regards to the following:`=` `\text(Undefined values of) 1/(\text(cos) x) \text(will be asymptotes)` `=` `\text(Defined values of) 1/(\text(cos) x) \text(will be points of intersection)` Finally, graph `y=\text(sec) x`Asymptotes`1/(\text(cos) pi/2)` `=` `\text(undefined)` `1/(\text(cos) 3pi/2)` `=` `\text(undefined)` Points of intersection`1/(\text(cos) 0)` `=` `1` `1/(\text(cos) pi)` `=` `1` `1/(\text(cos) 2pi)` `=` `1` Take note that the curves of `y=\text(sec) x` will keep approaching but will never intersect with the asymptotes. 
Question 2 of 4
2. Question
Graph the trigonometric function`y=3cos 2x`Hint
Help VideoCorrect
Correct!
Incorrect
General Form of a Cos Function
`y=``a` `\text(sin)` `b``x`Period Fomula
$$P_{\text{sin}}=\frac{2\pi}{\color{#00880A}{b}}$$First, identify the values of the function`y` `=` `a` `\text(cos)` `b``x` `y` `=` $$\color{#004ec4}{3}\;\text{cos}\;\color{#004ec4}{2}x$$ `a` `=` `3` `b` `=` `2` Next, solve for the period of the function$$P_{\text{cos}}$$ `=` $$\frac{2\pi}{\color{#00880A}{b}}$$ `=` $$\frac{2\pi}{\color{#00880A}{2}}$$ Substitute known values `=` `pi` To graph the `cos` curve, it is better to divide the value of its period into for parts and have the curve meet the following conditionsCurve starts at the peak of the amplitude `(a)`Curve intercepts xaxis at 1st quarterCurve reaches minimum amplitude at 2nd quarterCurve intercepts xaxis again at 3rd quarterCurve starts again at the period (`P=pi`)Therefore, this will be the `cos` curve for `y=3\text(cos) 2x` with a period of `pi` 
Question 3 of 4
3. Question
Graph the trigonometric function`y=4cos 2/3x`Hint
Help VideoCorrect
Well Done!
Incorrect
General Form of a Cos Function
`y=``a` `\text(sin)` `b``x`Period Fomula
$$P_{\text{sin}}=\frac{2\pi}{\color{#00880A}{b}}$$First, identify the values of the function`y` `=` `a` `\text(cos)` `b``x` `y` `=` $$\color{#004ec4}{4}\;\text{cos}\;\color{#004ec4}{\frac{2}{3}}x$$ `a` `=` `4` `b` `=` `2/3` Next, solve for the period of the function$$P_{\text{cos}}$$ `=` $$\frac{2\pi}{\color{#00880A}{b}}$$ `=` $$\frac{2\pi}{\color{#00880A}{\frac{2}{3}}}$$ Substitute known values `=` `(6pi)/2` `=` `3pi` To graph the `cos` curve, it is better to divide the value of its period into for parts and have the curve meet the following conditionsCurve starts at the peak of the amplitude `(a)`Curve intercepts xaxis at 1st quarterCurve reaches minimum amplitude at 2nd quarterCurve intercepts xaxis again at 3rd quarterCurve starts again at the period (`P=3pi`)Therefore, this will be the `cos` curve for `y=4\text(cos) 2/3x` with a period of `3pi` 
Question 4 of 4
4. Question
Graph the trigonometric function within the domain `pi/2≤x≤2pi``y=tan x`Hint
Help VideoCorrect
Nice Job!
Incorrect
Period Fomula
$$P_{\text{tan}}=\frac{\pi}{\color{#00880A}{b}}$$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` Asymptotes will occur within the domain for the values of `tan` that are undefined`\text(tan) pi/2` `=` `\text(undefined)` `\text(tan) pi/2` `=` `\text(undefined)` `\text(tan) 3pi/2` `=` `\text(undefined)` To graph the `tan` curve, start at the lower domain `(pi/2)` and draw a curve going passing through `(0,0)` and heading up to the second asymptote `(pi/2)`. This will cover a period of the curve.Repeat the process until you reach the upper domain `(2pi)`.First curveSecond curveThird curve
Quizzes
 Derivative of Trigonometric Functions 1
 Derivative of Trigonometric Functions 2
 Derivative of Trigonometric Functions 3
 Trig Applications of Differentiation
 Integral of Trigonometric Functions 1
 Integral of Trigonometric Functions 1
 Trig Applications of Integration
 Graph Trigonometric Functions 1
 Graph Trigonometric Functions 2
 Graph Trigonometric Functions 3
 Graph Trigonometric Functions 4