Download Name: Period: ______ Date: Group members: Honors Pre

Name: _____________________________________________________ Period: ________ Date: ___________________
Group members: ____________________________________________________________________________________
Honors Pre-Calculus 2012-13
Ms. York
Chapter 4 Test Review
Directions: Below are questions that will help you prepare for the Chapter 4 Test. There will be a calculator part and a noncalculator part for the test. Try to complete the exercises without a calculator where it states “No Graphing Calculator.”
Some formulas/definitions/identities that will be really helpful:
 radians
arc length r

time
t
central angle 

Angular Speed:  
time
t
1
Area of a Sector of a Circle: A  r 2
2
1
sec 
1
sec  
cos
1
sin  
csc 
1
csc  
sin 
sin 
tan  
cos
cos
cot  
sin 
x  cos
y  sin 
30-60-90 Triangle
45-45-90 Triangle
Convert degrees to radians: multiply by
180
180
Convert radians to degrees: multiply by
 radians
Arc Length: s  r
Linear Speed: v 
cos 
Section 4.1 – Radian and Degree Measure (No Graphing Calculator)
1. Convert 150 from degrees to radians and sketch the angle.
2. Convert 
9
from radian to degrees and sketch the angle.
4
Section 4.2 – Trigonometric Functions: The Unit Circle (No Graphing Calculator)
3. Find the exact values of the six trigonometric functions when

a.   
2
sin 2   cos 2   1
1  tan 2   sec 2 
1  cot 2   csc 2 
Amplitude = a
2
Period =
b
Phase Shift:
Left: bx  c  0
Right: bx  c  2
Vertical Shift: d
b.  
4
3
c.  
7
4
Section 4.3 – Right Triangle Trigonometry (No Graphing Calculator)
4. Find the exact values of the six trigonometric functions given the triangle.
sin  __________________________
cos  __________________________
tan  __________________________
csc  __________________________
sec  __________________________
cot   __________________________
5. Use trigonometric identities to transform the left side of the equation into the right side. ( 0   
tan   cot 
 csc 2 
tan 

2
)
Section 4.4 – Trigonometric Functions of Any Angle (No Graphing Calculator)
6. Find the exact value of
 
a. tan   
 3
 5 
b. tan  
 6 
 5 
c. sec  
 4 
7. Find the exact values of the other five trigonometric functions given sin   
1
and cos  0 .
2
cos  __________________________
tan  __________________________
csc  __________________________
sec  __________________________
cot   __________________________
Section 4.5 – Graphs of Sine and Cosine Functions (No Graphing Calculator)
8. Graph y  sin  . Determine its domain, range, amplitude, and period.
Domain:
Range:
Amplitude:
Period:
9. Graph y  cos . Determine its domain, range, amplitude, and period.
Domain:
Range:
Amplitude:
Period:
Section 4.6 – Graphs of Other Trigonometric Functions (No Graphing Calculator)
10. Graph y  csc  . Determine its domain, range, amplitude, and period.
Domain:
Range:
Amplitude:
Period:
11. Graph y  sec  . Determine its domain, range, amplitude, and period.
Domain:
Range:
Amplitude:
Period:
12. Graph y  tan  . Determine its domain, range, amplitude, and period.
Domain:
Range:
Amplitude:
Period:
13. Graph y  cot  . Determine its domain, range, amplitude, and period.
Domain:
Range:
Amplitude:
Period:
Section 4.7 – Inverse Trigonometric Functions (No Graphing Calculator)
14. Evaluate the expression. Keep your answer in radians.
 3
a. arccos 

 2 
b. arcsin(1)
15. Find the exact value of the expression. Keep answer in radians and rationalize if applicable.

 1
a. sin  arcsin   
 2

  3  
b. arcsin  sin   
  4 
c.

 12  
cot  arcsin    
 13  

16. Write an algebraic expression that his equivalent to (you do not need to rationalize)

 x
a. tan  arccos   
 2

b. sec(arcsin(x  1))
Section 4.8 – Applications and Models (Graphing Calculator Allowed)
17. An engineer erects a 75-foot cellular telephone tower. Find the angle of elevation to the tope of the tower at a point
on the level ground 50 feet from its base. Find the angle measure to the nearest tenth of degree.