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1330 Test 3 Review
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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. 10% 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!
1330 Test 3 Review
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1330 Test 3 Review
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1. Evaluate the following:
a) 32
sin3
b) 41
cos6
c) 63
tan4
d) 81
cot4
e) 25
sin6
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2. Evaluate the following:
a. sin(20 )
b. cos(61 )
c. 455cos 72 4sin 25 cos
2
d. 41
sin2
e. 27
sin2
Note: cos( ) 1n if n is even cos( ) 1n if n is odd sin( ) 0n for any n (even or odd)
If n is ODD, cos 02
n
.
If n is ODD, sin 12
n
or sin 12
n
depending on the quadrant!!! Check!
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Know inverse trig values! These are very quick questions if you understand the notion of “inverse trig functions”.
3. 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
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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
arc cos2 4
1arcsin
2 6
1 2
arccos2 3
arcsin 0 0 arccos 0 0
1arcsin
2 6
1
arccos2 3
2arcsin
2 4
2arccos
2 4
3arcsin
2 3
3arccos
2 6
arcsin 12
arccos 1 0
arctan 14
arctan 0 0
arctan 14
3arctan
3 6
arctan 33
arctan 33
3arctan
3 6
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4. Find the exact value of the following. If undefined, state, undefined.
a) sin cos
b) tan sin
c) 5
cot arcsin13
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5. 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
d) ( ) 4cot 5 1f x x
6. 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
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7. Give an equation of the form 𝑓(𝑥) = 𝐴 tan(𝐵𝑥 − 𝐶) + 𝐷 that could represent the following graph. a)
b)
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c)
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8. 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.
a)
b)
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9. Suppose that 2
cos( )5
x and 02
x
. Find the values of:
a) cos(2 )x
b) sin(2 )x
10. Given: tan( ) 10x and 02
x
, find the value of sin(2 )x .
1330 Test 3 Review
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KNOW the famous right triangles: 3-4-5, 5-12-13, 8-15-17; this saves time.
11. 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
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12. Given: 8
sin( )17
x and 02
x
, find the value of the following expressions using sum
and difference formulas:
a) sin3
x
b) cos4
x
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13. 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
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14. 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
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15. 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
16. Which of the following are true?
I. 2 21 tan ( ) sec ( )t t II. cos(2 ) 2cos( ) 1x x III. sin( ) sin( )x x
A) I only B) I and II only C) I, II, and III D) I and III only E) II and III only F) None of these
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17. 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.
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18. 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.