Download Trigonometry #1

Trigonometry
Chapter 1
Right Triangles
 Mr. Pines classroom room 802 is approximately 193
yards from the Main Office at Rancho.
 Mr. Patterson’s classroom is only 72 yards from Mr.
Pines classroom.
 These 3 locations form a triangle.
 Draw this triangle labeling all important information.
Are you having trouble drawing this triangle?
If you know where Mr. Patterson’s room it is possible.
 CASE 1
 Let’s consider that the angle formed at Mr. Patterson’s
room is a right angle. Does this help?
 How many different ways can you draw this triangle?
 Can you find the measure of the other 2 angles?
 If not the exact measures, can we estimate? What types of
angles are these?
 What should all the angles add up to?
 How far is Mr. Patterson’s room from the main office?
 What do we know for sure about this distance without
making an calculations?
 CASE 2
 Let’s say that some of the distances in CASE 1 were
incorrect. It appears that the angle formed at Mr.
Patterson’s room is a right angle, and that the angle
formed at the office is 30 degrees. The only correct
distance is that room 802 is 72 yards from Mr.
Patterson’s room.
 What is the relationship between the sides?
 Solve the remaining pieces of the triangle?
30-60-90 triangle
Hypotenuse = 2(short leg)
Long Leg = √3(short leg)
c) If the short leg is 9 feet, what are the lengths of the long leg and hypotenuse?
d) If the hypotenuse is 8 centimeters, what are the lengths of the two legs?
45-45-90 triangle
Hypotenuse = √2(leg)
a) If each leg is 8 ft, how long is the hypotenuse?
b) If the hypotenuse is √10 feet, how long is each leg?
Special Right Triangles
Special Right Triangles
Special Right Triangles
Special Right Triangles
Special Right Triangles
Special Right Triangles
Angles are supplementary……which means they add to 180 degrees.
What is the value of x?
The three angles ALWAYS
add up to 180 degrees.
a) If α=110° and β=45°, find γ
b) If γ=βand α=3β, find all three angles.
Pythagorean Theorem
a2 + b2 = c2
c) If a = 6 and c = 10, find b
d) If a = 6 and b = 5, find c
e) If b = √7 and c = 10, find a
NFL CHALLENGE
NFL CHALLENGE
As a group answer all questions on the NFL questionnaire
You do not need to write the city name, just the mascot
Example: Los Angeles Rams…...just write RAMS
Use your cell phones
Use Google, Find an NFL site, search for predictions, etc
After the SUPER BOWL in Febuary, we will see who wins,.....baseball
cards awarded to best group.....we will use this data in class later
You have 15 minutes.....GO
NFL CHALLENGE
Trigonometric Values
 SOH CAH TOA
Sin = Opp/Hyp
Csc = Hyp/Opp
Cos = Adj/Hyp
Sec = Hyp/Adj
Tan = Opp/Adj
Cot = Adj/Opp
Sin = y/r
Csc = r/y
Cos = x/r
Sec = r/x
Tan = y/x
Cot = x/y
a) Find the value of x.
b) Find the 6 trig function values.
Trigonometric Values
Find the 6 trig function values at the points:
a) (-4,5)
b) (2,5)
c) (-3,-10)
Solving Right Triangles
Solving Right Triangles
Solving Right Triangles
Solving Right Triangles
12
Solving Right Triangles
A
12.2
C
19.3
B
Solving Right Triangles
A
16
9
C
B
Solving Right Triangles
A
12.4
C
18.3
B
Solving Right Triangles
A
12.4
C
18.3
B
Solving Right Triangles
A
65° 41’
5.92
C
B
Solving Right Triangles
A
19
32° 23’ 29”
C
B
Google Maps
1. Using your cell phone find Rancho and 2 other locations in
Garden Grove that form a right triangle. Sketch the triangle
labeling all vertices, distances, and angle measures. Round side
lengths to the nearest tenth of a mile.
2. Using your cell phone find Rancho and 2 other locations in
Garden Grove that form a special right triangle. Either a 30-6090, or a 45-45-90 triangle. Sketch the triangle labeling all
vertices, distances, and angle measures. Round side lengths to
the nearest tenth of a mile.
 Hint: choose locations that are close to the street.
Degrees,Minutes,Seconds
1 Degree° = 60 Minutes’
1 Minute’ = 60 Seconds”
Ex1: Add the degrees and minutes
51° 29’ + 32°46’
Ex1: Add the degrees and minutes
90° - 73°12’
84°15’
16°48’
Conversions
Convert 34.817° to degrees, minutes, and seconds.
Conversions
Convert 74° 8’ 14” to decimal degrees.
Conversions Practice
To Deg,Min,Sec
a) 122.6853°
b) 89.9004°
To Decimal Degrees
c) 274° 18’ 59”
d) 165° 51’ 9”
Trigonometric Values
Find the 6 trig function values at the point (3,-4)
Trigonometric Values
 Find all 6 trig function values given the equation
3x-y = 0, x>0
Start out by choosing a convenient value for x.
Trigonometric Values
 Find all 6 trig function values given the following
equations:
a) 2x-5y = 0, x<0
b) 3x+7y =0, x>0