1. pencil, red pen, highlighter, calculator, notebook
U8D3
Have out:
pencil, red pen, highlighter, calculator, notebook
Bellwork:
Determine the value of x.
25° x 2 1) 2) 3)
20° x x 12 5 +1 +1 5 +1 +1 +1 +1
+1 exact +1 +1
+2 approx.
total: +2 +2

2. The _______ side will fall into one of the four __________. terminal
An angle θ is in _______ _______ on the xy–plane when its vertex is on the _______ and the ______ side is on the positive x–axis.
standard position
origin
initial
The _______ side will fall into one of the four __________.
terminal
quadrants y
(0, 0) x y I x II IV
III
terminal side
initial side

3. An angle is in:
90° 0°
90° y I x II IV
III
Quadrant I if ______ < < ______
90°
180°
Quadrant II if ______ < < ______
180° 0°
180°
270°
Quadrant III if ______ < < ______
Quadrant IV if ______ < < ______
270°
360°
270°
An angle whose terminal side falls on an axis is called a
_________ angle.
quadrantal
The _________ angles are _____, _____, _____, _____, …
quadrantal 0°
90°
180°
270°

4. Practice: In which quadrant or on which axis does the terminal
side of each angle lie? Draw a sketch.
1) 140°
2) 210°
3) 300°
4) 450° y x y x y x y x
Huh? Isn’t that 90o? II
III IV
positive y–axis
Negative angles go in a ________ direction.
5) –200°
6) –120°
7) –180°
clockwise y x y x y x II
III
negative x–axis

5. Radian Measure
Given a circle with center O and radius r, draw a central angle
such that the arc length is equal to the radius.
(Hint: Use string and a protractor.)
The measure of the angle is defined as __________. r
one radian r O r
How many degrees is one radian???

6. One radian is approximately ______ degrees.
57.3
One radian is approximately ______ degrees.
Since the formula for the circumference of a circle is ________, there are ___ radians in one complete revolution of a circle.
(let r = radians)

7. We know there are _____ in a circle, so _____ = _____ radians,
or more simply, _____ = _____ radians.
360o
360o
180o
360o
Now, solve for r.
 We use this conversion when we go from _______ to _______.
1 radian =
≈ _____
57.3o
radians
degrees
 We use this conversion when we go from _______ to _______.
1° =
radians
degrees
radians

8. Practice: Convert each to radian measure.
1) 90°
2) 270°
3) 60°
4) 120°
5) 200°

9. Practice: Convert each to degree measure.1) 2) 3) 4) 5)
NOTE: If you do not label the degree symbol, it is assumed that answer is in radians. Your answers will be marked incorrect!

10.  Record the radian measure on each of the _________ angles.
quadrantal
An angle is in:
Quadrant I if ______ < < ______ y I x II IV
III
Quadrant II if ______ < < ______
Quadrant III if ______ < < ______
Quadrant IV if ______ < < ______

11. I II IV Practice: In which quadrant or on which axis does the terminal
side of each angle lie? Convert to degrees. 1) 2) 3) y x y x y x I II IV

12. Practice: In which quadrant or on which axis does the terminal
side of each angle lie? Convert to degrees. 4) 5) 6) y x y x y x
negative y–axis IV
III

13. Complete the rest of the worksheets.