Download Chapter 5

Section 5.1 – Angles and Degree Measure
Objectives:
1. Convert decimal degree measures to degrees, minutes, and second and vice versa.
2. Find the number of degrees in a given number of rotations.
3. Find coterminal angles to a given angle.
I. Standard Position
A. Initial Sides
B. Terminal Sides
C. Vertex
D. Quadrantile Angles
E. Reference Angles
Find the reference angles for 295° and –325°
F. Coterminal Angles
Find one positive and one negative coterminal angle for 42° and 215°.
II. Angle Measures and Rotations
A. Degree (°), minute (’), and second (”)
1. 60’ =
2. 60” =
3. 3600” =
B. Rotations – 1 rotation =
C. Examples
1. Convert 329.125° to DMS
2. Convert 35° 12’ 7” to DD
3. Give and angle measure for 6.75 rotations.
Homework: p. 280 – 3, (18-57)/3, 58, 61, 63, 68-76 evens
Honors Precalculus
Chapter 5
Page 1
Section 5.2 – Right Triangles
Objectives:
1. To find values of trigonometric functions for acute angles.
2. To solve triangles involving right angles
Review – __________-__________-__________
SOH -- sin
Reciprocal -- csc
CAH -- cos
Reciprocal -- sec
TOA -- tan
Reciprocal -- cot
Examples
1. A right triangle has sides whose lengths are 8-cm,
8
15-cm, and 17-cm. Find the value of the six trig function of .
17

15
2. Use a calculator to find the following:
a. sin 34° 12’ 13”
b. cot 43°
Homework: p.288 – 1, 9, 11-29 odds, 30-35 all
Honors Precalculus
Chapter 5
Page 2
Section 5.3A – Circular Trigonometry Review
Review:
How can you right sin θ , cos θ, and tan θ using ( x, y ) and r (radius)
Sin θ =
Cos θ =
Tan θ =
Examples:
Find the values of the six trig functions of an angle in standard position with measure
with coordinates (-15,8) lies on its terminal side.
Find sin
If sec
when cos
2 and
5
and the terminal side of
13
, if the point
is in the first quadrant.
lies in quadrant IV, find tan .
Homework: p. 296 – 1, 30-36 all, 38-44 all, 50, 51, 53-59 odds
Honors Precalculus
Chapter 5
Page 3
Section 5.3B – Circular Function (Trig Functions of General Angles)
Work Together
Label the sides of the triangles with the exact value and then state the ratio.
1
6
1
12
______:_____:______
______:_____:______
Does the ratio change because the size (length of the sides) of the triangle changes?
Fill in the following chart with exact values for the reference angles using information we discussed
today and yesterday.
Radian
Degree
0
0°
/6
30°
/4
45°
/3
60°
/2
90°
Sin
Cos
Tan
Fill in the following chart to indicate the sign of trig functions in each quadrant.
S
A
T
C
I
II
III
IV
sin & csc
Wrap Up
cos & sec
tan & cot
Think and Discuss
Draw the angle in standard position, draw the reference angle, and find the exact value of the trig
function.
sin 315
tan 240
sec
390
csc 270
Homework: p. 296 – 14-29 all, 37, 45, 47 – ignore the unit circle comment
Note: when asking for exact values this means do not use your calculator.
Honors Precalculus
Chapter 5
Page 4
Section 5.4 and 5.5 – Applying Trigonometric Triangles and Solving Right Triangles
Objectives:
1. To solve triangles involving right angles
A
Examples
1. Solve:
52
C
B
12
T
12
2. In RST, find mR.
S
10
R
3. Assuming the ladder of a ladder truck is mounted 8-ft off the ground, what is the tallest
building which the 108-ft ladder can reach using the optimum operating of 60? How
far away from the building would the ladder be placed?
4. A regular hexagon is inscribed in a circle with diameter 8.2-cm. Find the apothem.
Note: apothem is the measure of a line segment drawn from the center of the regular
polygon to the midpoint of one of its sides.
5. A flagpole 50-ft high stands on top of the Lewis Building. From a point P in front of
Carroll’s Drugstore, the angle of elevation of the top of the pole is 5822’ and the angle
of elevation of the bottom of the pole is 4612’. How high is the building?
Homework: Day 1: p.301 – 1, 3, 11-23 odds, 25-27 all, 30-36 all
6. cos sin
1
3
2
7. tan arccos
10. Solve for x: cos x
1
2
8. tan sin
1
4
5
9. cos arccos
2
5
1
2
Homework: Day 2: p.309 – 15-27 all, 31, 40, 44, 45,47, 49
Honors Precalculus
Chapter 5
Page 5
Section 5.6 – Law of Sine
Objectives:
1. To solve non right ’s (ASA, AAS) using the Law of Sines
2. To solve the ambiguous non right  (SSA) using Law of Sines
A
Law of Sines
c
b
B
Proof:
a
C
112 , and x
22 .
A
c
b
h
B
Examples
C
a
1. AAS – Solve: XYZ if m X
29 , m Y
2. ASA – A person in a hot-air balloon observes that the angle of depression to a
building on the ground is 65.8°. After ascending vertically 500 feet, the person now
observes that the angle of depression is 70.2°. How far is the balloonist now from
the building?
3. Find the area for the example 1.
Homework: p. 316 – 11-23 odds, 28, 30-34, 36-38 all
Honors Precalculus
Chapter 5
Page 6
Section 5.7 – The Ambiguous Case for the Law of Sines
Objective:
1. To solve the ambiguous non right  (SSA) using Law of Sines
The Ambiguous Triangle (SSA)
A. Case 1: m A 90
1. Situation a: If
2. Situation b: If
3. Situation c: If
a) and a
b) and a
B. Case 2: m A 90
1. Situation a: If
2. Situation b: If
C. Examples:
a
b
a b sin A , then one solution (a right triangle).
a b sin A , then no solution.
a b sin A ,
b , then one solution.
b , then two solutions.
A
b
a b , then no solution.
a b , then one solution.
a
a
A
1. SSA – Solve: ABC, if
A 72 14 , b
2. SSA – Solve: ABC, if
A 58 , b 14 , and a 10 .
3. SSA – Solve: ABC, if
A 32 , b 11 , and a
22 , and a
21 .
7.
Homework: p.324 – 11-17 all, (18-30)/3, 35, 36, 38, 41, 42
Honors Precalculus
Chapter 5
Page 7
Section 5.8 – Law of Cosines
Objectives:
3. To solve non right ’s (SAS and SSS) using the Law of Cosines
Review – Law of Cosines
___ 2 ___ 2 ___ 2 2 ____ cos___
___ 2
___ 2
___ 2 2 ____ cos___
___ 2
___ 2
___ 2 2 ____ cos___
A
c
B
b
a
C
A
Proof:
c
b
h
x
a-x
B
C
a
Examples
1. SAS – Suppose you want to fence a triangular lot as shown. What is the length of the
fence?
78’
102
2. SAS – Solve: XYZ if m X
84’
39 24 , y 12 , and z 14 .
3. SSS – Solve: RST, if r 19 , s
24.3 , and t
21.8 .
Homework: p.330 – 11-29 odds, 32-38 all
Honors Precalculus
Chapter 5
Page 8