1330 review test3 - math.uh.edualmus/1330_review_test3.pdf · microsoft word -...

1330 Test 3 Review Dr. Almus

Math 1330 Test 3 Review

Where: CASA (see your conformation email for the exact location)

Time: 50 minutes

Questions: ___ Multiple Choice + ___Free Response = Total ___

Points: Multiple Choice: ____ pts, Free Response: _____ pts.

What is covered? Chapter 5, and 6.1, 6.2.

What to bring? Cougar card Make up Policy: NO MAKE-UPS! Plan to be at the testing center 10-15 minutes before your scheduled time. If you are late, then try to reschedule through your CASA account. If you miss your test, you will get a zero for the test. Your Final exam score will replace ONE lowest score test grade. There will be a formula sheet available during the exam. It is your responsibility to locate it before starting the exam. If you can’t find the link for it, ask proctors for help. A copy of it is on the next page so you know what to expect on the test. How to study? Begin with this review. Take Practice Test 3 BEFORE your test! It is for practice AND extra credit. 5% of your best score will be added to your Test 3 score. Know how to write COMPLETE answers to free response problems. NO skipping steps! KNOW UNIT CIRCLE!


This formula sheet will be available during the test:


1. Evaluate the following:

a) 32

sin3

b) 41

cos6

c) 43

tan4

d) 21

cot4

e) 25

sin6

f) sin(20 )

g) cos(61 )

h) 5cos 72 4sin 25


Know inverse trig values! These are very quick questions if you understand the notion of “inverse trig functions”.

2. Evaluate the following:

a) 3

arcsin2

b) 1

arccos2

c) arctan 1

d) 2

arcsin2

e) 1 3cos

2

f) arctan 1

g) 1

arcsin2

h) 1 2

arcsin arccos2 2

i) 1arctan 1 arcsin

2


The following table lists the most common “inverse trig” function values. Make sure you know these and understand why these are true. If you know the unit circle, you know the values listed here; you just need to think “backwards” and know the range restrictions.

arcsin 12

arccos 1

3arcsin

2 3

3 5

arccos2 6

2arcsin

2 4

2 3

arccos2 4

1arcsin

2 6

1 2

arc cos2 3

arcsin 0 0 arccos 0 0

1arcsin

2 6

1

arc cos2 3

2arcsin

2 4

2arc cos

2 4

3arcsin

2 3

3arc cos

2 6

arcsin 12

arccos 1 0

arctan 14

arctan 0 0

arctan 14

3arctan

3 6

arctan 33

arctan 33


3arctan

3 6

3. Find the exact value of the following. If undefined, state, undefined.

a) sin cos

b) tan sin

c) 5

cot arcsin13


4. Find the periods of the following functions:

a) ( ) 2sin 4 1f x x

b) ( ) 4cos 1 52

xg x

c) ( ) 2 tan 1f x x

5. Give an equation of the form 𝑓 𝑥 𝐴 cos 𝐵𝑥 𝐶 𝐷 which satisfies the following description. “The amplitude is 3, the phase shift is 2 to the left, vertical shift is 4, and the period is .”

a) 𝑓 𝑥 3 cos 6𝜋𝑥 12 4 b) 𝑓 𝑥 3 cos 6𝑥 12 4 c) 𝑓 𝑥 6 cos 3𝜋𝑥 12 4 d) 𝑓 𝑥 3 cos 6𝑥 12 4 e) 𝑓 𝑥 6 cos 6𝑥 2 4


6. Give an equation of the form 𝑓 𝑥 𝐴 tan 𝐵𝑥 𝐶 𝐷 that could represent the following graph. a)

b)


c)

7. For the following graph give an equation of the form 𝑓 𝑥 𝐴 sin 𝐵𝑥 𝐶 𝐷 which

could be used to represent the graph.


8. Suppose that 2

cos( )5

x and 02

x

. Find the values of:

a) cos(2 )x

b) sin(2 )x

9. Given: cot( ) 6x and 02

x

, find the value of sin(2 )x .

10. Given: 5

sin( )13

x and 02

x

, find the value of the following expressions using sum

and difference formulas:

a) sin4

x

b) cos6

x


c) sin3

x

d) 3

cos4

x

11. Given: 4

sin( )5

x , 12cos

13y and 0 ,

2x y

, find the value of the following

expressions using sum and difference formulas: sin x y

12. Simplify the following expressions:

a) 2 2

40sin( ) cos( )

cos sin

x x

x x

b) 2 25sin 5cos 7 tan( )cot( )x x x x

c) 60sin( ) cos( )t t

13. State whether the following equations are TRUE or FALSE: ________ sin( ) sin( )x x ________ cos( ) cos( )x x

________ 2 21 tan ( ) sec ( )t t


________ sin(2 ) 2sin( )x x ________ tan( ) tan( )x x ________ cos(2 ) 2cos( ) 1x x

________ 2 2sin ( ) 1 cos ( )x x ________ sin( ) sin( )x x ________ cos( 20 ) cos( )x x ________ tan( 45 ) tan( )x x

14. Graph 𝑓 𝑥 2 cos 8𝑥 for one period. a) State the period. b) Label the x and y intercepts (if any) with ordered pairs. c) Label the maximum value(s) (if any) with an ordered pair. d) Label the minimum value(s) (if any) with an ordered pair. e) State the domain of the function. f) State the range of the function.

15. Graph 𝑓 𝑥 6sin 4𝑥 for one period.

a) State the period. b) Label the x and y intercepts (if any) with ordered pairs. c) Label the maximum value(s) (if any) with an ordered pair. d) Label the minimum value(s) (if any) with an ordered pair. e) State the domain of the function. f) State the range of the function.

1330 review test3 - math.uh.edualmus/1330_review_test3.pdf · microsoft word -...

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