6.6E: Graphs of the Other Trigonometric Functions (Exercises)
- Page ID
- 99754
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Section 6.2 Exercises
Match each trigonometric function with one of the graphs.
1. \(f\left(x\right)=\tan \left(x\right)\)
2. \(f\left(x\right)=\sec \left(x\right)\)
3. \(f\left(x\right)=\csc (x)\)
4. \(f\left(x\right)=\cot \left(x\right)\)
I 
II
III 
IV
Find the period and horizontal shift of each of the following functions.
5. \(f\left(x\right)=2\tan \left(4x-32\right)\)
6. \(g\left(x\right)=3\tan \left(6x+42\right)\)
7. \(h\left(x\right)=2\sec \left(\dfrac{\pi }{4} \left(x+1\right)\right)\)
8. \(k\left(x\right)=3\sec \left(2\left(x+\dfrac{\pi }{2} \right)\right)~\)
9. \(m\left(x\right)=6\csc \left(\dfrac{\pi }{3} x+\pi \right)\)
10. \(n\left(x\right)=4\csc \left(\dfrac{5\pi }{3} x-\dfrac{20\pi }{3} \right)\)
11. Sketch a graph of #7 above.
12. Sketch a graph of #8 above.
13. Sketch a graph of #9 above.
14. Sketch a graph of #10 above.
15. Sketch a graph of \(j\left(x\right)=\tan \left(\dfrac{\pi }{2} x\right)\).
16. Sketch a graph of \(p\left(t\right)=2\tan \left(t-\dfrac{\pi }{2} \right)\).
Find a formula for each function graphed below.
17. 
18. 
19. 
20. 
21. If \(\tan x=-1.5\), find \(\tan \left(-x\right)\).
22. If \(\tan x=3\), find \(\tan \left(-x\right)\).
23. If \(\sec x=2\), find \(\sec \left(-x\right)\).
24. If \(\sec x=-4\), find \(\sec \left(-x\right)\).
25. If \(\csc x=-5\), find \(\csc \left(-x\right)\).
26. If \(\csc x=2\), find \(\csc \left(-x\right)\).
Simplify each of the following expressions completely.
27. \(\cot \left(-x\right)\cos \left(-x\right)+\sin \left(-x\right)\)
28. \(\cos \left(-x\right)+\tan \left(-x\right)\sin \left(-x\right)\)
- Answer
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1. II
3. I
5. Period: \(\dfrac{\pi}{4}\). Horizontal shift: 8 right
7. Period: 8. Horizontal shift: 1 left
9. Period: 6. Horizontal shift: 3 left
11.
13.
15.
17. \(f(x) = 2 \sec(\dfrac{\pi}{2} x) - 1\)
19. \(f(x) = 2 \csc(\dfrac{\pi}{4} x ) + 1\)
21. \(\tan(-x) = 1.5\)
23. \(\sec(-x) = 2\)
25. \(\csc(-x) = 5\)
27. \(-\csc(x)\)