AAT Honors
2nd Semester Spiral Review
Mrs. Iverson
Name _____________________________
Date ______________ Period _________
Unit 3 Part A – Trig Part 1
#1-2: Use the diagram to the right to answer the following questions.
1.
a) Find the value of sin A __________
1a. __________
b) Find the value of tan A __________ C
1b. __________
c) Find the value of sec A __________
2. Solve for  A to the nearest degree.
B
1c. __________
10
8
A
2. ___________
#3 - 14 : Trig review.
3. Find x.
3. __________
6
18°
x
4. Convert 240 to radian measure.
5. Convert
9
radians to degree measure.
4
6. Give a positive & negative coterminal with a –50 angle in standard position.
4. ___________
5. ___________
6. ___________
___________
7. Given ABC with a = 18, b = 24, and C = 72, find the measure of c using
the Law of Cosines.
7. ___________
8. Given ABC, C = 50, b = 32, and c = 25, solve for  B using Law of Sines.
8. ___________
9. The Bermuda Triangle is a region of the Atlantic Ocean between
Bermuda, Miami, Florida, and San Juan, Puerto Rico. It is an area where ships
and airplanes have been rumored to mysteriously disappear.
What is the distance between Miami & Bermuda?
9. ___________
10. Find the exact value of tan 210.
10. __________
11. Find the exact value of csc
12. If sin  

.
2
4
and  is in Quadrant II, find cos .
5
11. __________
12. __________
13. Find the exact value of the six trig functions containing the point (-3, 5).
13. _________________________________________________________________________
14. Find tan  if cos  
3

and
 
7
2
14. __________
#15 - 17: Angle of Elevation and Depression Application Problems.
15. Jim is going to climb a rock wall. Right now he is looking at the wall from a point 50 ft from the
base of the wall. He measures the angle of elevation to the top of the tower to be 65 . How tall is
the rock climbing wall? Round to the nearest tenth.
15. ______________________
16. While in Chicago, Derrick Rose wants to know how far from the Sears Tower he is. He knows that
the tower is 1,450 feet tall. The angle of elevation from where he is standing to the top of the tower
is 60°. How far away is he?
16. ______________________
17. A dog is looking at a cat in a tree. He is 20 feet away and the cat is 30 feet up in the tree. What
is the angle of elevation he has to look up to see the cat?
17. ______________________
#18-20: Solve triangle ABC using the given measurements. Round measures of sides to the
nearest tenth and measures of angles to the nearest degree.
18.
B  49 , C  90 , a  9
A  _____ b  _____ c  _____
A'  _____ b '  _____ c '  _____
19.
a  16, b  7, c  12
A  _____ B  _____ C  _____
A'  _____ B '  _____ C '  _____
20.
A  42 , a  22, b  12
B  _____ C  _____ c  _____
B'  _____ C '  _____ c '  _____
#21 - 23: Application
21. Find the area of a triangle lot with two sides of lengths 90 meters and 52 meters and an included
angle of
102
.
21. ______________________
22. A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle
of elevation to the top of the tree as 71.5 . How tall is the tree?
22. ______________________
23. You are 200 yards from a river. Rather than walking directly to the river, you walk 400 yards
along a straight path to the river’s edge. Find the acute angle

between this path and the
river’s edge.
(river’s edge)
23. ____________________
Unit 3 Part B – Trig Part 2
#24 - 26: Graph the following trig functions.
24. Sketch y  3tan(
x 
 )  2 in the interval [0, 2 ].
2 4
1. Curves =
________________
4. TYP?=
________________
2. Period =
________________
5. I.L. =
________________
3. M.P. =
________________
6. V.T. =
________________
7. K.P. =
________________
25. Sketch two cycles of y  2sin(2 x)  3 .
1. Amp =
________________
4. TYP?=
________________
2. Period =
________________
5. I.L. =
________________
3. B.P. =
________________
6. V.T. =
________________
7. K.P. =
__________________________
26. Sketch one cycle of the function
y   csc( x  3 ) .
1. Amp =
________________
4. TYP?=
________________
2. Period =
________________
5. I.L. =
________________
3. B.P. =
________________
6. V.T. =
________________
7. K.P. = __________________________
Unit 3 Part C – Trig Part 3
#27-28: Simplify the given trig functions.
27.
sin 2  cot 2 
1- sin 2 
28.
sin 
1- cos 
+
1- cos 
sin 
#29-30: Verify.
tan 
29.
 cos   sec 
csc 
tan 2   1
30.
 sec2   tan 2 
sin  tan  sec   1
# 30-31: Solve the trig function with the given constraint.
30. Solve the trig equation sin  cos = sin  for all values of  in radians.
2
2
31. Solve the trig equation sin   cos  for all values of  in degrees.