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

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Jan 2, 2021
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- 6.2: Graphs of the Other Trig Functions
- 6.3: Inverse Trigonometric Functions

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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 $屏幕快照 2019-07-09 上午4.10.09.png$ II $屏幕快照 2019-07-09 上午4.10.28.png$

III $屏幕快照 2019-07-09 上午4.10.47.png$ IV $屏幕快照 2019-07-09 上午4.11.08.png$

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. $屏幕快照 2019-07-09 上午4.12.29.png$ 18. $屏幕快照 2019-07-09 上午4.14.13.png$

19. $屏幕快照 2019-07-09 上午4.14.33.png$ 20. $屏幕快照 2019-07-09 上午4.14.56.png$

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. $Screen Shot 2019-10-11 at 1.59.39 PM.png$

13. $Screen Shot 2019-10-11 at 2.00.14 PM.png$

15. $Screen Shot 2019-10-11 at 2.01.07 PM.png$

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. $-\csc(x)$

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