Download Trigonometry – Cumulative Review #1 Chapter 9 : Trig Basics

Name ______________________________________________ Date________
Trigonometry – Cumulative Review #1
Chapter 9 : Trig Basics
What you need to know!!
Special Right Triangles: Use to find exact trig
values of 30 , 45 , 60 .
The Unit Circle: use to find trig functions of
quadrantal (multiple of 90 ) angles
All Student Take Calculus: Tells you which trig
function is positive in which quadrant. Please
note: a trig function’s RECIPROCAL function
has the same sign (+/-)
SOHCAHTOA
The buttons sin-1, cos-1, and tan-1 will give you
the angle when you know the value of the trig
function. There are no buttons for sec -1, csc-1,
and cot-1.
1. Find
Ans: 4/3
3. Find
Ans:
Sec is the reciprocal of cos
Csc is the reciprocal of sin
Cot is the reciprocal of tan
2. Find
Ans: 5/4
4. Find cos A if b=16, a=12, c=20 where
is the right angle.
Ans: 4/5
C
Name ______________________________________________ Date________
5. Use the appropriate trigonometric ratio
to find the value of x.
Ans: 10.5
7. Use the appropriate trigonometric ratio
to find the value of
6. Use the appropriate trigonometric ratio to
find the value of .
Ans: 68
8. The angle of elevation to the top of the
empire state building from a distance 1 mile
away is 11 . Find the height of the building
to the nearest foot.
Ans: .19 miles
Ans: 46
9. In what quadrant is 160 ?
Ans: II
11. Find a positive coterminal angle for 100
Ans: 260
13. Find
10. In what quadrant is -130 ?
Ans: III
12. In what quadrant is angle
tan
?
and
Ans: III
14. The point (9, -40) is a point on the
terminal ray of an angle in standard form
on the coordinate plane. Find the sin of
the angle.
Ans: -40/41
Ans: -2/3
if sin
Name ______________________________________________ Date________
15. If sin
tan .
where
is in quadrant II, find
Ans:
17. What is the reference angle for 200 ?
16. Find the exact value of
2cos30 + 4 tan 60
Ans:
18. Find the exact value of sin 210
Ans: -1/2
Ans: 20
19. Find the exact value of csc 120
20. Find the exact value of cot 315
Ans: :
Ans: -1
Name ______________________________________________ Date________
Trigonometry – Cumulative Review #2
Chapter 10: Radians
What you need to know!!
Relationship between a central angle and an
arc:
where S=length of arc, is the
measure of the central angle in radians, and
the radius of the circle.
is
Cofunctions have angles that are
complementary (add to 90 ). Sine and Cosine,
Tangent and Cotangent, and Secant and
Cosecant are cofunctions.
Example: sin 20 = cosine 70 .
1. The radius of a circle is 10”. Find the
length of an arc intercepted by a
central angle of 2 radians.
To convert from degrees to radians: multiply
by
To convert from radians to degrees: multiply
by
You also need all of the information
from the Chapter 9 Cumulative Review
Handout!
2. Convert 40 to radians.
Ans: :
Ans: :
3. Convert
4. Find the exact value of sin .
to degrees.
Ans: :
Ans: :
5. Find the exact value of cos .
6. Find the exact value of tan .
Ans: :
Ans: :
7. Find the exact value of sin
Ans: :
.
8. Find the exact value of tan
Ans: :
.
Name ______________________________________________ Date________
9. If
, find
.
Ans: :
10. Find the exact value of csc
.
Ans: :
11. If sin 3x=cos 7x, find the value of x.
12. If tan (x+20) =cot (3x- 40 ), find the value of x.
Ans: :
Ans: :
Name ______________________________________________ Date________
Trigonometry – Cumulative Review #2
QUIZ Chapter 9/10
1. Draw the unit circle here, and label the
2. Draw the special right triangles here,
coordinates at the quadrantal (multiple of
labeling the angles AND the sides.
90 ) angles.
3. Convert
to radians.
5. Find the exact value of tan
ALL WORK.
4. Convert
, showing
7. If sec (x+10 )=csc (3x-20), find the value
of x. Show your work.
to degrees.
6. Find the exact value of sec
showing ALL WORK.
8. What is the reference angle for
250 ?
,
Name ______________________________________________ Date________
Trigonometry – Cumulative Review #3
“Cheating” with your calculator for MULTIPLE CHOICE problems.
Press MODE, and make sure it is set to DEGREES mode.
In order to do this, you MUST memorize these decimal approximations:
(I’m hoping you already know that ½ = .5 exactly.)
Using a calculator to help you, find the exact value of
1. Sin 30
2. Cos 30
3. Tan 30
4. Sin 60
5. Cos 60
6. Tan 60
7. Sin 45
8. Cos 45
9. Tan 45
Using a calculator is great because they you don’t have to do all that reference
angle and ATSC stuff to find the exact value of angles greater than 90 . Just type
it in the calculator!!
10. Sin 150
11. Cos 150
12. Tan 150
13. Sin 315
14. Cos 315
15. Tan 315
16. Sin 240
17. Cos 240
18. Tan 240
You can also find the exact values in this manner if the problem is given in
radians. Just make sure you press MODE, and make sure it is set to RADIANS
mode.
19. Sin
20. Cos
21. Tan
22. Sin
23. Cos
24. Tan
Name ______________________________________________ Date________
Your calculator can find the exact trig value of any quadrantal angle. Use the
appropriate mode of your calculator to find the exact value of:
25. Sin 0
26. Cos 90
27. Tan 180
28. Sin
29. Cos
30. Tan
You can use these values to help you find the exact reciprocal trig functions as
well.
31. cot 0
32. csc 90
33. sec 180
34. csc 270
35. sec 360
36. cot 90
37. cot 30
38. csc 60
39. sec 45
40. csc 150
41. sec 135
42. cot 300
Name ______________________________________________ Date________
Trigonometry Homework:
USE YOUR CALCULATOR to get the exact value of the following. Make sure
your MODE is set to radians or degree when it is necessary.
1. Sec 0
2. Cos 90
3. csc 45
4. tan 60
5. cot 30
6. tan 135
7. sin 330
8. Cos 315
9. Sec 210
10. Cos 240
11. Sec
12. Cos
13. csc
14. tan
15. sec
16. cos
Name ______________________________________________ Date________
Trigonometry – Cumulative Review #4
Chapter 9, 10 using the calculator to help!!.
1. Find
Ans: 5/4
3. Find
Ans:
5. Use the appropriate trigonometric
ratio to find the value of x to the
nearest tenth.
Ans: 10.5
7. In what quadrant is 300 ?
Ans: IV
9. Find a positive coterminal angle for
-30
Ans: 330
2. Find
Ans: 3/4
4. Find cot A if b=16, a=12, c=20 where
C is the right angle.
Ans: 4/3
6. Use the appropriate trigonometric ratio
to find the value of to the nearest
degree.
Ans: 68
8. In what quadrant is -100 ?
Ans: III
10. In what quadrant is angle
and cos
?
Ans: IV
if sin
Name ______________________________________________ Date________
11. Find sin
12. The point (9, -40) is a point on the
terminal ray of an angle in standard
form on the coordinate plane. Find the
cos of the angle.
Ans: 9/41
Ans:
13. If sin
where
find cos .
14. Find the exact value of
2cos30 + 4 tan 60
is in quadrant II,
(recall you can use your calculator to help you get the exact
values if you remember the decimal approximations)
Ans:
Ans:
15. What is the reference angle for 250 ?
16. Find the exact value of sin 240
Ans:
Ans:70
17. Find the exact value of sec 120
Ans: -2
19. Find the exact value of sin 90
Ans:1
21. Convert 50 to radians
Ans:
18. Find the exact value of sin 315
Ans:
20. Find the exact value of tan 270
Ans: undefined
22. Convert
Ans:120
to degrees
Name ______________________________________________ Date________
23. Determine the exact value of tan
.
Ans:
24. Determine the exact value of sin
.
Ans:
25. Determine the exact value of sec
Ans: undefined
27. If
Ans: 70
.
26. Determine the exact value of csc
.
Ans:
, find x.
28. If
Ans:
, find x.
Name ______________________________________________ Date________
What you need to know!! Chapter 9 and 10
Special Right Triangles: Use to find exact trig
values of 30 , 45 , 60 .
The Unit Circle: use to find trig functions of
quadrantal (multiple of 90 ) angles
All Student Take Calculus: Tells you which trig
function is positive in which quadrant. Please
note: a trig function’s RECIPROCAL function
has the same sign (+/-)
The buttons sin-1, cos-1, and tan-1 will give you
the angle when you know the value of the trig
function. There are no buttons for sec -1, csc-1,
and cot-1.
SOHCAHTOA
Sec is the reciprocal of cos
Csc is the reciprocal of sin
Cot is the reciprocal of tan
Relationship between a central angle and an arc:
where S=length of arc, is the measure of the central
angle in radians, and is the radius of the circle.
To convert from degrees to radians: multiply by
Cofunctions have angles that are complementary (add
to 90 ). Sine and Cosine, Tangent and Cotangent, and
Secant and Cosecant are cofunctions.
Example: sin 20 = cosine 70 .
You also need all of the information from the
Chapter 9 Cumulative Review Handout!
To convert from radians to degrees: multiply by
(I’m hoping you already know that ½ = .5 exactly.)
Name ______________________________________________ Date________
Trigonometry
PRACTICE QUIZ #2 Chapter 9/10
1. Draw the unit circle here, and label
the coordinates at the quadrantal
(multiple of 90 ) angles.
3. Convert
to radians.
2. Draw the special right triangles here,
labeling the angles AND the sides.
4. Convert
to degrees.
Ans:
Ans:
5. Find the exact value of tan
6. Find the exact value of sec
Ans:
Ans:
7. If sin (x+10 )=cos (3x-20), find the value
of x. Show your work.
8. What is the reference angle for
100 ?
Ans:
Ans:
Name ______________________________________________ Date________
Trigonometry
QUIZ #2
1. Draw the unit circle here, and label
the coordinates at the quadrantal
(multiple of 90 ) angles.
3. Convert
to radians.
5. Find the exact value of tan
7. Find
Chapter 9/10
2. Draw the special right triangles here,
labeling the angles AND the sides.
4. Convert
to degrees.
6. Find the exact value of csc
8. Find cot A if b=6, a=8, c=10
where C is the right angle.
Name ______________________________________________ Date________
9. Use the appropriate trigonometric
ratio to find the value of x to the
nearest tenth.
10. Use the appropriate
trigonometric ratio to find the
value of to the nearest degree.
15
50
5
2
11. In what quadrant is 250 ?
12. In what quadrant is -200 ?
13. Find a positive coterminal angle for
-50
14. In what quadrant is angle
sin
and tan
?
if
Name ______________________________________________ Date________
Trigonometry – Cumulative Review #5
Chapter 11 – Trig Graphing
Standard form of a trig equation:
What you need to know!!
is the amplitude
b is the frequency
d is the midline shift
is the period
Period =
Vocabulary
amplitude: how high above the midline the
graph reaches
Frequency: how many complete cycles of sine
or cosine you see from 0 to
Period: how long it takes to make one cycle of
a sine or cosine curve
Midline: the horizontal center of the graph
and frequency=
sine
cosine
a is
+
a is
-
Determine the equation of each of the following.
Name ______________________________________________ Date________
Equation
1.
2.
3.
4.
5.
Amplitude
Frequency
Period
midline