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6.2.2E: Graphs of the Other Trigonometric Functions (Exercises)


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

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. $$-\csc(x)$$