6.2.2E: Gráficas de las Otras Funciones Trigonométricas (Ejercicios)

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Sección 6.2 Ejercicios

Haga coincidir cada función trigonométrica con una de las gráficas.

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 $2019-07-09 4.10.09.png$ II $2019-07-09 4.10.28.png$

III $2019-07-09 4.10.47.png$ IV $2019-07-09 4.11.08.png$

Encuentra el periodo y desplazamiento horizontal de cada una de las siguientes funciones.

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. Esboce una gráfica de #7 arriba.

12. Esboce una gráfica de #8 arriba.

13. Esboce una gráfica de #9 arriba.

14. Esboce una gráfica de #10 arriba.

15. Esbozar una gráfica de$j\left(x\right)=\tan \left(\dfrac{\pi }{2} x\right)$.

16. Esbozar una gráfica de$p\left(t\right)=2\tan \left(t-\dfrac{\pi }{2} \right)$.

Encuentre una fórmula para cada función graficada a continuación.

17. $2019-07-09 4.12.29.png$ 18. $2019-07-09 4.14.13.png$

19. $2019-07-09 4.14.33.png$ 20. $2019-07-09 4.14.56.png$

21. Si$\tan x=-1.5$, encuentra$\tan \left(-x\right)$.

22. Si$\tan x=3$, encuentra$\tan \left(-x\right)$.

23. Si$\sec x=2$, encuentra$\sec \left(-x\right)$.

24. Si$\sec x=-4$, encuentra$\sec \left(-x\right)$.

25. Si$\csc x=-5$, encuentra$\csc \left(-x\right)$.

26. Si$\csc x=2$, encuentra$\csc \left(-x\right)$.

Simplifica completamente cada una de las siguientes expresiones.

27. $\cot \left(-x\right)\cos \left(-x\right)+\sin \left(-x\right)$

28. $\cos \left(-x\right)+\tan \left(-x\right)\sin \left(-x\right)$

Contestar

1. II

3. I

5. Periodo:$\dfrac{\pi}{4}$. Desplazamiento horizontal: 8 a la derecha

7. Periodo: 8. Desplazamiento horizontal: 1 izquierda

9. Periodo: 6. Desplazamiento horizontal: 3 a la izquierda

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

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

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

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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