Embed Size (px)
Citation preview
Start PlayingJeopardy
Final Jeopardy
Triggy Identities G-UnitGrrrraff’s
How HOT are you feeling?
Created by Adam Garry, Co-nect
100 100 100 100 100
200 200200200200
400
300300300 300300
400400400400
500 500500500500
.
Category 1 100
Answer
€
Sin2(ϑ ) +Cos2(ϑ ) = ???
Answer Category 1 100
1
Answer
Category 1 200
€
Sin(ϑ ) =
Answer Category 1 200
€
=y
r=
1
Csc(ϑ )
Category 1 300
Answer
€
2
Cos2(35o)−
2
Cot 2(35o)=
Answer Category 1 300
2
Category 1 400
Give the following criteria:
Find
Answer
€
Tan (ϑ ) < 0
Sec(ϑ ) =5
3
€
Cos(2ϑ )
Answer Category 1 400
€
−7
25
Category 1 500
Evaluate the following Expression.
Answer
€
Cot(200o)Tan (−20o)
Answer Category 1 500
-1
What is the definition of a degree?
Category 2 100
Answer
Answer Category 2 100
A degree is a form of measure when two rays form a vertex.
It is a measure of an angle.
Category 2 200
What is a radian?
Answer
Answer Category 2 200
A radian is the length of the radius around the circumference (Arc Length) of a circle.
It is another measure of an angle.
Category 2 300
Convert the following from radians to degrees.
Answer
€
π5
=
5π
2=
Answer Category 2 300
€
π5
= 36o
5π
2= 450o
Category 2 400
Answer
How many radians are in a circle?
Answer Category 2 400
A little more than 6…
To be exact
€
2π
Category 2 500
If the central angle of a circle is
and the radius is 7 inches, what is the Arc Length and the area of the sector?
Answer
€
60o
Answer Category 2 500
€
S =7π
3in.
A =49π
6in.2
Category 3 100
What is the period, domain and range of ?
Answer
€
f (x) = Sin(x)
Answer Category 3 100
€
period = 2π
Domain = (−∞,∞)
Range = [−1,1]
Category 3 200
What are the asymptotes of ?
Answer
€
f (x) = Tan (x)
Answer Category 3 200
€
Asymptotes = ±π
2,±
3π
2,±
5π
2,...
Category 3 300
What is the similarity of a Sine and Cosine graph?
Answer
Answer Category 3 300
The Sine function is a Phase Shift of the Cosine function shifted to the right
The Cosine function is a Phase Shift of the Sine function shifted to the left.
€
π2
€
π2
Category 3 400
Describe the transformations that occur to the following function.
Answer
€
f (x) = −6Sin(2x −π ) + 3
= −6Sin(2(x −π
2)) + 3
Answer Category 3 400
Period (Horizontal Compression):
Phase Shift: right
Amplitude (Vertical Stretch): 6
Reflected over x-axis
Vertical Shift: Up 3€
π
€
π2
Category 3 500
Answer
What transformation occurred to the following graph? What is an equation for this graph? HINT: Do not worry about horizontal shifts, horiz. compressions, or horiz. stretches.
Answer Category 3 500
€
f (x) = −6Cos(x)
The amplitude increased to 6. There was a vertical stretch.
Category 4 100
What is the radius of the Unit Circle?
Answer
Answer Category 4 100
1
Category 4 200
Evaluate the following.
Answer
€
Cosπ
3
⎛
⎝ ⎜
⎞
⎠ ⎟
Answer Category 4 200
€
1
2
Category 4 300
Evaluate the following Trigonometric Expression.
Answer
€
Tan (−3π
4)
Answer Category 4 300
1
Category 4 400
Evaluate the following:
Answer
€
Tan43π
6
⎛
⎝ ⎜
⎞
⎠ ⎟
Answer Category 4 400
€
1
3=
3
3
Category 4 500
Answer
€
Cos5π
4
⎛
⎝ ⎜
⎞
⎠ ⎟Sin
π
6
⎛
⎝ ⎜
⎞
⎠ ⎟
Answer Category 4 500
€
6
4
Category 5 100
What is the Period for the following function?
Answer€
f (x) = −6Cos(3x)
Answer Category 5 100
€
2π
3
Category 5 200
What is a Phase Shift?
Answer
Answer Category 5 200
A Phase Shift is a horizontal shift in a trig. Function. It is represented by the following symbols: OR
€
φw
€
C
Β
Category 5 300
Answer
What is the amplitude and y-intercept of the following?
€
f (x) = −4
3Sin(3x −
π
2)
Category 5 400
What is the Phase Shift of the following equation? Explain, in words, what happens.
Answer
€
f (x) = −4Cos(2π (x −2
π))
Answer Category 5 400
The Cosine graph moves to the right.
The local maxima is no longer on the y-axis but is when x =€
2
π
€
2
π
Category 5 500
Answer
Solve the following equation:
€
Sin(3ϑ + 2) =Cos(ϑ − 2) +1
Answer Category 5 500
€
x ≈ −2.472
or
x ≈ −1.780
or
x ≈ −.623
or
x ≈ .123
Final Jeopardy
Answer
Final Jeopardy Music
Given the following Scenario: Suppose that the length of time between consecutive high tides is approximately 10.5 hours. According to the National Oceanic and Atmospheric Administration, on Saturday, August 23, 2008, in South Padre Island, Texas, high tide occurred at 2:45 AM (2.75 hours) and low tide occurred at 8:04 AM (8.067 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 9.3 feet, and the height of the water at low tide was -0.9 foot. Write a sinusoidal function for the situation above.
Answer Final Jeopardy
€
f (x) = 5.1Sin4π
21(x + .125)
⎛
⎝ ⎜
⎞
⎠ ⎟+ 4.2
€
f (x) = 5.1Sin4π
21x + 5.42
⎛
⎝ ⎜
⎞
⎠ ⎟+ 4.2
€
2π
10.5=
4π
21
Daily Double
Answer
Answer Daily Double
€
4
3Amplitude:
Y-intercept:
€
−4
3
