Download Test Outlines

Outline for Test #1-Trig
Part 1 has 15 questions that you may NOT use a calculator. These are trig functions of the
special angles and the quadrantal angles. Like p. 64: 10-43 AND p. 66: 71-82
Part 2 has 12 questions that you may use a calculator.
1.
2.
3.
4.
5.
6.
7.
8.
Convert to DD (decimal degrees). P. 8: 45-56
Convert to DMS. P. 9:57-68
Find the angle of smallest possible positive measure coterminal with the given angle. P. 9: 69-88
Find the exact values of the six trigonometric functions for the angle in standard position having the
following point as its terminal side. P. 27: 1-20
Find the exact values of all the other trigonometric functions for the angle given. P 38: 69-78
Find a solution for the equation. Assume that the following angles are acute. P. 56:27-36
Find the reference angle for each of the following: p. 63:1-6
Use a calculator to find approximations of each of the following. P. 68: 5-19
9. Find the angle in the interval [0 ,90 ) that satisfies the following. P. 68: 23-31
10. & 11. Solve the right triangle:
12. Problem like p.43:41, 43, 49, 51
p. 79: 9-13, 21-35
Outline for Test #2-Trig
Part 1 has 16 questions that you may NOT use a calculator.
You will have to fill in the order pairs of the first quadrant of the unit circle.
You will have questions like 63-82 on P. 107 AND like 7-22 P. 126
You will have questions like 61-66 on P. 127
Part 2 has 16 questions that you may use a calculator.
1. Find h in the figure. P. 89: 27-29
2&3. Convert each of the following degree measures to radians.
Leave answers as multiples of  . P. 106: 7-18
4 &5. Convert each of the following radian measures to degrees. P. 107: 25-40
6-8 Use a calculator to find each of the following to four decimal places. P. 126:23-34
 


9-10. Find the value of s in the interval  0,  that makes the following true. Round to four
2
decimal places. P. 127: 55-60
11. Find the distance between 2 cities. P.113: 21-24
12. Two gears. P. 114: 27-32
13. Find the linear speed. P. 133: 29-34
14. Two pulleys. P. 134: 40
15 & 16. Graph a sine and cosine function over a one period interval. P. 153-154: 13-39
Outline for Test #3-Trig
Questions 1,2,3: Graph 3 of the 6 trig functions.
Questions 4-13: Write out the Pythagorean Identities, Sum and Difference Identities, Double
Angle Identities.
Question 14: Find the exact value of the cosine of an angle using Sum and Difference Identities.
Like # 5-8 p. 222
Question 15: Find the exact value cos( A  B ) . Simplify your answer.
Like #47-52 p. 222
Question 16: Find the exact value of sin(   ) . Simplify your answer.
Like #41-46 p. 230
Question 17: Find the exact value of tan(   ) . Simplify your answer.
Like #47-52 p. 222
Question 18: Find the exact value of sin 2. Simplify your answer.
Like #12-16 p. 239
Question 19: Find the exact value of sin  . Simplify your answer.
Like #7-10 p. 239
Question 20: Find the exact value of tan 2 . Simplify your answer.
Like #12-16 p. 239—on the homework you were asked to find just sin and cosine. On the
test I am asking for the tangent value.
Questions 21 and 22: Verify. I will give you 4 to choose from.
Outline Test #4-Trig
Section 5.6: 2 like p. 246 (19-29) You do not need to memorize the half-angle identities
Section 6.1: 6 like p. 270 (13-45) You do not need to memorize the intervals.
Section 6.1: 1 like p. 272 (77-85)
Section 6.2 and 6.3: solve 8 equations. You will need to know the double angle identities for sin
and cosine. You will need to know the Pythagorean identities. You will need to know the
quadratic formula.
Section 7.1, 7.2, 7.3: 5 problems—solving for parts of triangles.
Trigonometry
Math 1316
Review for Exam 4
5.6, 6.1, 6.2, 6.3, 7.1, 7.2, 7.3
 3
3
 
with
   2 . Simplify your answer.
 , given that cos  
5
2
2
4

 
with
    . Simplify your answer.
2. Find the exact value of tan   , given that sin  
2
5
2
1. Find the exact value of sin 
(3-8: Finding the inverse function values.)
Give the exact real number value of y.
 2
 2 


3. y  arc cos 
5.
4. y  cot
  arc csc( 2)
Use a calculator to give each real number value.
7.
y  arc csc( 3.5641)
6.
1
(  3)

  tan 1  

3

3 
Give the exact value of the following:
8.
1 

sec  sin 1 
5 

Solve each of the following equations in the interval [ 0 , 360 ) . Give exact values where appropriate. Express
approximate answers to nearest tenth of a degree.
2
2
9. 6sin   2  sin 
10. csc   3 cot   5
11.
5cos 2   4 cos  2
12.
sin 2 
 2
2
13. 8  csc 3  4 csc 3
Find the indicated part of each triangle ABC (some problems may have more than one solution or no solution.)
14. A  35, B=53, b=675cm; find a
15. A=51.2, c=7986 cm, a= 7208 cm; find B
16. a=95 ft, b= 112 ft, c= 180 ft; find C
17. C=65, a=160 cm, b= 125 cm; find B
Answers

5 3
1. sin 
2
10
2. tan

2
3
3. y=
4
5
4. y 
6
5.  
2


6
7. y  .28439
8.
11. 110.4 ,249.6
12. 112.5 ,157.5 ,292.5 ,337.5
13. 12.9 ,132.9 ,252.9 ,47.1 ,167.1287.1
14. a  484.8
15. B =29.1or 8.5
16. C  120.6
17. B  46.6
4
6.   
10. 14 ,135 ,194 ,315
5 6
12
9. 41.8 ,138.2 ,150 ,330