Download 4/29 Unit Circle guided notes File

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Sequential Trigonometry
The Unit Circle
Guided Notes
In a 45-45-90 triangle,
hypotenuse = leg × √2

Special Right Triangle Formulas
In a 30-60-90 triangle,
In a 30-60-90 triangle, the
hypotenuse = short leg × 2
long leg = short leg ×√3
The unit circle is the set of points _____________ away from the origin.
o It has center ________ and radius _____.
Ex. 1:
a) Draw a 45º angle in standard position.
Draw in the right triangle with base on the x-axis.
b) What is the length of its hypotenuse?
c) What is the length of its legs?
d) What are the coordinates of the point where the
terminal side of the angle intersects the unit circle?

That point is called the terminal point.
Ex. 2:
a) Draw a 30º angle in standard position.
Draw in the right triangle with base on the x-axis.
b) What is the length of its hypotenuse?
c) What is the length of its short leg?
d) What is the length of its long leg?
e) What are the coordinates of the terminal point?
Ex. 3:
a) Draw a 60º angle in standard position.
Draw in the right triangle with base on the x-axis.
b) What is the length of its hypotenuse?
c) What is the length of its short leg?
d) What is the length of its long leg?
e) What are the coordinates of the terminal point?
For a non-acute angle θ, its reference angle is the _________________, __________________ angle
formed by the terminal side and ___________________.

If our given angle is called θ, its reference angle is called θ ' (read “____________________”).
Examples: Sketch the angles. Then find their reference angles.
1) 150º
3) 8π/3
2) -100º
4)
-5π
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Extension
For the 45º-45º-90º triangle…
1. Reflect that triangle over the y-axis (Quadrant II).
a. What is the value of the standard-position angle
that gets you to that terminal side?
b. What are the coordinates of the terminal point?
2. Reflect that triangle over the x-axis (Quadrant III).
a. What is the value of the standard-position angle
that gets you to that terminal side?
b. What are the coordinates of that terminal point?
3. Reflect the original triangle over the y-axis (Quad IV).
a. What is the value of the standard-position angle that gets you to that terminal side?
b. What are the coordinates of that terminal point?
For the 30-60-90 triangle with 30º in standard position…
4. Reflect the triangle into the second quadrant.
a. What is the value of the standard-position angle
that gets you to that terminal side?
b. What are the coordinates of that terminal point?
5. Reflect the triangle into the third quadrant.
a. What is the value of the standard-position angle
that gets you to that terminal side?
b. What are the coordinates of that terminal point?
6. Reflect the triangle into the fourth quadrant.
a. What is the value of the standard-position angle that gets you to that terminal side?
b. What are the coordinates of that terminal point?
For the 30-60-90 triangle with 60º in standard position…
7. Reflect the triangle into the second quadrant.
a. What is the value of the standard-position angle
that gets you to that terminal side?
b. What are the coordinates of that terminal point?
8. Reflect the triangle into the third quadrant.
a. What is the value of the standard-position angle
that gets you to that terminal side?
b. What are the coordinates of that terminal point?
9. Reflect the triangle into the fourth quadrant.
a. What is the value of the standard-position angle that gets you to that terminal side?
b. What are the coordinates of that terminal point?