Name Date

Pre-Cal Test Review

4,7-4.8 & Sinusoidal Applications

Period

Section 4.7- Inverse Trig Functions KNOW YOUR FLASHCARDS!

• Evaluate Trig Functions (without circle or calculator)

_ ÿr ÿ-31. sinZC - 3 2. cos -3 ol. 6 ÿ

K3. tan--=

4

llzc ÿ6. sin--= --6 °;

(4): --'- ÿ -ÿ-ÿ7. sin - \-ÿ, 8. cos--=

4 ' ....

9. tan--= - v3 ', D

Evaluate Inverse Trig Functions (without circle or calculator)

o Remember: Restricted Domains• Sin: ÿ":ÿ -" (ÿ ÿ ÿ-'

• Cos: c" ÿ ÿ ÿv

• Tan: ÿ-,,ÿ C" ÿ-- n-y).

10. arcsin =-ÿ, 11. cos-1 - -ÿ-i 12. arctan = --

13. sin-l(1)= iÿ 14. arccos - : =ÿ=)

15. tan-1 (1)= -7`°

16. arcsin - = -1ÿ_.. 17. cos-ÿ 0 = - 18. arctan(ÿ-

• Composition Functions

19. sin arcsin - ÿ 20. cos-1 cos - ,ÿ 21. arctan an - = .ÿ

22. cos 23. tan/ 24. sin (arcc.

3 -% 1%, ! ÿ::

12;'4

27. tan<arccos )

i ;t

L<;..... 1

k --J

C<"% 4 '-:ÿ _, , xt

30. arctan 4ÿ)

L L/

• Use inverse trig function to write 0 as a function ofx

31. 32.

x+6

12-\ ( Iÿ\

o: tÿ"ÿ, L%

x-8

33.

2x+7

o = [o_,, ! 'ÿ'ÿ -l/

Section 4.8 - Applications

• Right Triangle Word problems

34. The height of a radio transmission tower is 10 meters, and it casts a shadow of length 30 meters. Find

the angle of elevation of the sun.

0 Iÿ

35. Your football has landed at the edge of the roof of your school building. When you are 25 feet from the

base of the building, the angle of elevation to your football is 21°. How high off the ground is your football?

X

;95

• Bearings

o Drawinÿ Bearings

Draw these bearings (be as accurate as possible)36. N25°E 37. $75°W 38. N 45° W

Wÿ. ........

/ --ÿE VVÿ--.ÿ ...... ÿE

S

39. 80° 40. 185° 41. 315°

VVÿ .......

o Labelinÿ Bearings

Label each bearinÿ in two ways (nautical and air)

42.

Wÿ ..........

43.

s

% ÿ ÿJ° w

........... ÿE

45.

VVÿ -ÿE

S S

o Word Problems

46. A ship is 45 miles east and 30 miles south of port.

should be taken? How long will the trip be?The captain wants to sail directly to port. What bearing

0ÿ" ÿ o.ÿ ......

_mÿ___ I[\' 5,_o,, ÿ < 1

47. An airplane is 160 miles north and 85 miles east of an airport. The pilot wants to fly directly to the airport.

What bearing should betaken? How long will the trip be?Ic.ÿv,J,_,

Sinusoidal Applications

.i_cÿ ("it = \, IlO0,ÿ-t-'ÿ< :

48. A Ferris wheel is built such that the height h (in feet) above the ground of a seat on the wheel at time

t (in seconds) can be modeled by h(t)=-65cos ÿ +70

a. Find the period of the model. What does the period tell you about the ride?

rÿ/,a J i"ÿ' ÿOtt,,_ÿt:.,ÿ,-, l il g-'-t %-"ÿ oi,ct,<ÿ,

B. Find the amplitude of the model. What does the amplitude tell you about the ride?

49.

c. Find the height a seat on the Ferris wheel at 12 seconds.

-.. ( 7G-0 5 -15

A Ferris wheel is built such that the height h (in feet) above the ground of a seat on the wheel at time

t (in seconds) can be modeled by h(t) =-42.5cos +57.5

a. Find the period of the model. What does the period tell you about the ride?

<..qr-c ----tcc-. < -t-4,'ÿ {ÿ--ÿ-ÿ"1% '+-:ÿw-ÿ--\ Oÿrvÿ>k-"A--ÿ<;ÿ orÿ:

V\ t.c t. t.ÿc- c c-,ÿ tct,O

v c- c. 0 [ t.,,ÿ-i Oi,.]

B. Find the amplitude of the model. What does the amplitude tell you about the ride?

c. Find the height a seat on the Ferris wheel at 40 seconds.