Algebra Exec Prep Trigonometric Ratios and the Unit Circle Questions This is a Alg2 assignment. I have attached the pdf to complete. This assignment came w
Algebra Exec Prep Trigonometric Ratios and the Unit Circle Questions This is a Alg2
assignment. I have attached the pdf to complete.
This assignment came with a very short video presentation. You DO NOT
have access to the video, so I have include the transcript of the video
to help you complete. It is pretty simple and will not require more than
an hour or so of time. Thank you in advance for accurate information.
Attached is a pdf of the transcript of the video, then the actual questions that need to be answered. 535
A Better Way?
Scenario: UNIT CIRCLE
Instructions:
View the video found on page 1 of this journal activity.
Using the information provided in the video, answer the questions below.
Show your work for all calculations.
The Students’ Conjectures: Joy and Kelvin want to find csc where
= 120 degrees. Complete the table to
summarize what you know about each student’s ideas regarding how to solve the problem. (2 points: 1 point for
each row of the chart)
Classmate
Conjecture
Joy
Kelvin
Analyze the conjecture:
1. What do you think? Does it makes sense that sin( ) = sin ? (1 point)
Analyze the Data:
2. What is 120 degrees in radians? (1 point)
3. Find csc(120). (2 points: 1 point for setup, 1 for final answer)
4. Now consider
= 120. Draw the angle
= 120 on the circle below. Make sure you rotate clockwise for the
negative angle. It needs to be approximate, but not precise. (1 point)
5. What reference angle in the first quadrant corresponds to
angle, 1 for radians)
=120? Answer in radians. (2 points: 1 for correct
6. What are the coordinates of the terminal point corresponding to
coordinate numbers, 1 for correct signs)
= 120 ? (2 points: 1 for correct
7. Use the Pythagorean theorem to prove that this point lies on the unit circle. (2 points: 1 point for correct
setup, 1 for correct calculation)
8. Find csc( ) where
= 120. (2 points: 1 for correct setup, 1 for final answer)
Making a Decision:
9. Who was correct? Does csc(120) = csc(120)? Explain. (2 points)
10. Do you think a similar rule is true for cosine? That is, does cos( ) = cos( )? Pick a value of
this theory. (2 points: 1 point for demonstrating with a value of , 1 point for conclusion)
11. Using your example above, speculate on a rule that might be true for cos( ). (1 point)
and test
Transcript: A Better Way?
This video begins with a woman talking in front of a blank screen.
Audio:
Hi, I’m Joy. Kelvin and I are working on the unit circle.
[An image is shown of a circle with a radius of 1.]
On-screen text: The unit circle
I’m trying to be upbeat about it, [A smiley face appears] but Kelvin’s just looking at
the negative angle. [The smiley face turns to a frown]
To be fair, the angle is negative.
We’re supposed to find the cosecant of negative 120 degrees. [On-screen text:
Problem: Find
where
]
We can’t use our calculators. All we have is the unit circle with the reference
angles. [An image is shown of the unit circle with the reference angles.]
Kelvin wants to measure 120 clockwise, and then use the reference angle on the
unit circle. I have a clever idea. I think we can find the cosecant of 120 and then
make it negative.
On-screen text:
Joy thinks:
Audio:
Kelvin’s not so sure. [A frowning face is shown beside the words “Kelvin thinks.”]
I noticed this rule: the sine of a negative angle is always equal to the negative of
the sine.
At least it looks like a rule to me. Kelvin’s still not sure. [A surprised face appears.]
But look: If theta is any angle, then negative theta goes the opposite way. [An
image is shown of a graph of a positive angle in the first quadrant. Above the angle
is written “Quadrant
.”] Clockwise, right? [The same angle is duplicated in the
fourth quadrant. Beneath the angle is written “Quadrant
.”]
The y-coordinates are always in opposite top and bottom quadrants. So the sine of
the negative angle is always negative of the sine. See?
Kelvin still doesn’t see. [A surprised face appears.] We know this: Cosecant equals
one over sine. And if I’m right that sine of negative theta equals negative sine
theta, then my idea is that cosecant of negative theta equals negative cosecant
theta. Obvious!
What do you think? Am I right? Unit circles are fun, right?
On-screen text:
Is Joy correct?
Does
?
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