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Mathematics LibreTexts

6.2E: Graphs of the Other Trigonometric Functions (Exercises)

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    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 image IIimage

    III image IVimage

    Find the period and horizontal shift of each of the following functions. \[5. f\left(x\right)=2\tan \left(4x-32\right)6. g\left(x\right)=3\tan \left(6x+42\right)7. h\left(x\right)=2\sec \left(\frac{\pi }{4} \left(x+1\right)\right)\] \[8. k\left(x\right)=3\sec \left(2\left(x+\frac{\pi }{2} \right)\right)~\] \[9. m\left(x\right)=6\csc \left(\frac{\pi }{3} x+\pi \right)10. n\left(x\right)=4\csc \left(\frac{5\pi }{3} x-\frac{20\pi }{3} \right)\]

    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 \(j\left(x\right)=\tan \left(\frac{\pi }{2} x\right)\).

    16. Sketch a graph of \(p\left(t\right)=2\tan \left(t-\frac{\pi }{2} \right)\).

    Find a formula for each function graphed below.

    17. image18. image

    19. image20. image

    1. If \(\tan x=-1.5\), find \(\tan \left(-x\right)\).

    2. If \(\tan x=3\), find \(\tan \left(-x\right)\).

    3. If \(\sec x=2\), find \(\sec \left(-x\right)\).

    4. If \(\sec x=-4\), find \(\sec \left(-x\right)\).

    5. If \(\csc x=-5\), find \(\csc \left(-x\right)\).

    6. 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. \(\cos \left(-x\right)+\tan \left(-x\right)\sin \left(-x\right)\)Section 6.3 Inverse Trig Functions 429