
# 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 II

III IV

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

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. 18.

19. 20.

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