Download Ferris Wheel

Use properties of similar triangles to explain
sine, cosine, and tangent
Define sine, cosine, and tangent in terms of
ratios
Explain how trigonometric ratios and
relationships help in solving problems
Use trigonometric relationships to solve real
world problems
 Using right triangles
Translate trigonometric functions to
represent a scenario
Relate sine and cosine by explaining their
relationship with:
right triangles,
unit circle,
sine/cosine waves
Explain 𝑠𝑖𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃 = 1 using
Pythagorean Theorem and the unit circle
 Angles of elevation and depression
 Sine and Cosine waves
Write a sine value in terms of cosine and
vice versa
SIMILAR TRIANGLES ACTIVITY
Learning Target: Use properties of similar triangles to explain sine, cosine, and
tangent
Discovering Trigonometry – Class Activity
WRAP UP: reflect on the learning target in your own words
TRIGONOMETRIC RATIOS
Learning Target: Define sine, cosine, and tangent in terms of ratios
Ratio table What are some possible applications of this tool?
WRAP UP: What are sine, cosine, and tangent? Create a triangle and describe where
you can “see” these relationships.
UNIT ASSESSMENT ESSAY QUESTION #1
1. Explain how sine, cosine, and tangent relate to similar triangles. Use diagrams,
tables, numbers, and words to justify your reasoning.
APPLICATIONS
Learning Targets:
Use trigonometric relationships to solve real world problems
 Using right triangles
 Angles of elevation and depression
PRACTICE APPLYING TRIGONOMETRY
Please complete this for class tomorrow
Practice 1 (No context)
Practice 2 (with context)
ANGLE OF THE SUN TASK
PAPER REQUIREMENTS
1. Hypothesis
2. Methods
3. Diagrams and angles
4. Minimum of 2 graphs + analysis of each
1.Time vs angle
2.Time vs shodow
5. Sources of error in results
6. Conclusions
OVERLAPPING CIRCLES PRE-TASK FOR 1ST SUMMATIVE
SETTING UP SPRINKLERS
Summative Task (can be worked on collaboratively, must be turned in individually)
UNIT ASSESSMENT - ESSAY QUESTION #2
2. Define sine, cosine, and tangent and explain how trigonometric ratios help in
solving problems. Provide examples of being given two sides versus given a side
and an angle. Use diagrams, tables, numbers, and words to justify your
reasoning.
DOMINGO’S RIDE
DOMINGO GETS ON AT POINT A
Domingo rides the Ferris
wheel at the fair. It has a
radius of 36 feet. When
Domingo gets on the
Ferris wheel it is 4 feet
above the ground. How
far above the ground is
Domingo at each point on
the Ferris wheel?
CREATE A GRAPH THAT DESCRIBES DOMINGO’S PATH
What relationships are noticeable
here?
What connections can you make
between the unit circle and the
ratios on the trig table?
Sine and Cosine waves as related to the unit circle
Learning Target: Understand Sine and Cosine waves as a function
Learning Target: Relate sine and cosine by explaining their relationship with:
right triangles, unit circle, sine/cosine waves
Get out 2 pieces of graph paper, your unit circle, and your trig table
Each page needs to be horizontal
Scale your x –axis from zero to 360 degrees.
Scale your y – axis from -1 to 1 (use a small increment, around .1)
Plot the graph of the sine ratios from zero degrees to 360 degrees on one page
and plot cosine graph on the other.
Sine Wave Video
WRAP UP: Reflect on the relationships on the sine and cosine graph and the
relationships between them.
TRANSLATE COS(𝜃) INTO THE FOLLOWING
f(x) = - cos(𝜃)
f(x) = cos(-𝜃)
f(x) = cos(𝟐𝜃)
f(x) = cos(𝜃/2)
f(x) = 5cos(𝜃)
f(x) = cos(𝜃) +10
f(x) = - cos(𝜃 - 90)
Please use a graphing calculator or desmos.com to
graph and compare these translations of cosine
When the term inside the brackets gets divided by 2 the cosine wave gets stretched by a
factor of two. I can generalize that the divisor when inside the brackets will stretch my
wave by the factor it divides by.
GRAPHING SINE AND COSINE
Can you write a function that represents Domingo’s place on the wheel as a function
of time?
Use sin or cosine (x) - not both, then translate your equation to fit the graph.
HOW CAN WE SEE THIS IDENTITY REPRESENTED IN A…?
Learning Target: Explain 𝑠𝑖𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃 = 1 using
Pythagorean Theorem and the unit circle
•
•
•
•
Unit Circle
Sine and Cosine waves
Right Triangles
Trig Table
Wrap up:
Note the places and ways we can see the trig identity
𝑠𝑖𝑛2 𝜃 + 𝑐𝑜𝑠 2 𝜃 = 1 in each representation.
UNIT ASSESSMENT – ESSAY #3
3. Explain the relationship between sine and cosine. How does the unit circle show the relationship?
How do the sine and cosine wave show the relationship? How can the sine of an angle be related to
the cosine of an angle? How is the trigonometric identity 𝒔𝒊𝒏𝟐 𝒙 + 𝒄𝒐𝒔𝟐 𝒙 = 𝟏 related to different
representations? Use diagrams, tables, numbers, and words to justify your reasoning.
SINE AND COSINE COMPLEMENTS POWERPOINT
UH – OH! I NEED TO REASSESS, NOW WHAT?
Complete the following practices prior to reassessing – all work must be shown
1. Finding sides using trig - Practice
2. Finding angles using inverse trig functions – Practice
3.
What is the unit circle – Watch video and write a reflection.
4. How are similar triangles related to trigonometry – Watch video and write
reflection
5. How can I use trig functions to solve problems - Watch video and write reflection