ExamView - 4.5-4.7 Review Sheet H.tst

Name: ________________________ Class: ___________________ Date: __________

ID: A

4.5-4.7 Review Sheet H Short Answer 1. Find the period and amplitude.

7. Write an equation for the function that is

described by the given characteristics.

y  8 sin20x

A sine curve with a period of  , an amplitude 2. Find the relationship between the graphs of f

of 4, a right phase shift of

and g . Consider amplitude, period, and shifts.



2

, and a vertical

translation up 2 unit.

f (x )  sinx

8. Consider the functions given by

g (x )  sin (x  3 )

f (x )  3 sinx

3. Find the relationship between the graphs of f

and g . Consider amplitude, period, and shifts.

and

f (x )  cos x

g (x )  3 csc x

1

g (x )  cos 5x

on the interval (0,  ) . Describe the behavior of each of the functions as x approaches  .

4. Find the relationship between the graphs of f

and g . Consider amplitude, period, and shifts.

9. State the period of the function.

f (x )  cos 7x

y  sec 2x

g (x )  3  cos 7x

10. State the period of the function.

5. Select the graph of the function. (Include two

full periods.) y  tan

y  sin5x 6. g is related to a parent function

x 3

11. Determine whether the function is even, odd,

f (x )  sin(x ) or f (x )  cos (x ).

or neither.

g (x )  cos (4x   )  3

f (x )  5 sec x

Describe the sequence of transformations from f to g.

12. Evaluate the expression. Round your result to

two decimal places. arccos 0.27

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Name: ________________________

ID: A

13. Evaluate the expression. Round your result to

18. Use the properties of inverse trigonometric

two decimal places.

functions to evaluate the expression.

arctan25

tan(arctan95)

14. Evaluate the expression. Round your result to

19. Use the properties of inverse trigonometric

two decimal places.

functions to evaluate the expression. arcsin(sin  )

cos 1 0.24 15. Evaluate the expression. Round your result to

20. Find an algebraic expression that is equivalent

two decimal places.

to the expression.

ˆ 1 Ê tan ÁÁÁ  300 ˜˜˜ Ë ¯

sec (arctan4x )

16. Use an inverse trigonometric function to write

 as a function of x .

ax b4 17. Use an inverse trigonometric function to write

 as a function of x .

ax b7

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ID: A

4.5-4.7 Review Sheet H Answer Section SHORT ANSWER 1. ANS:

Period:

 10

; Amplitude: 8

PTS: 1 2. ANS:

REF: 4.5.13

PTS: 1 3. ANS:

REF: 4.5.19

g is a shift of f 3 units to the right.

The period of f is 5 times the period of g . PTS: 1 4. ANS:

REF: 4.5.23

g is a shift of f 3 units downwards. PTS: 1 5. ANS:

REF: 4.5.26

PTS: 1 6. ANS:

REF: 4.5.44

ÈÍ ÍÍ  3 One cycle of g (x ) corresponds to the interval ÍÍÍÍ , ÍÍ 4 4 Î units. PTS: 1

REF: 4.5.63a 1

˘˙ ˙˙ ˙˙˙ and g (x ) is obtained by shifting f (x ) upward 3 ˙˙ ˙˚

ID: A 7. ANS:

y  2  4 sin(2x   )

PTS: 1 8. ANS:

REF: 4.5.83

PTS: 1 9. ANS:

REF: 4.6.65b

f approaches 0 and g approaches  .



PTS: 1 10. ANS:

REF: 4.6.9

PTS: 1 11. ANS:

REF: 4.6.10

3

Even PTS: 1 12. ANS:

REF: 4.6.57

1.30 PTS: 1 13. ANS:

REF: 4.7.23

1.53 PTS: 1 14. ANS:

REF: 4.7.28

1.33 PTS: 1 15. ANS:

REF: 4.7.30

–1.51 PTS: 1 16. ANS:

  arctan PTS: 1 17. ANS:

  arccos PTS: 1

REF: 4.7.39

x 4 REF: 4.7.43

7

x REF: 4.7.44 2

ID: A 18. ANS:

95 PTS: 1 19. ANS:

REF: 4.7.50

0 PTS: 1 20. ANS:

REF: 4.7.53

16x 2  1 PTS: 1

REF: 4.7.70

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