2-20-24 Rotation and Radian Measure

P4 A. The initial side lies along the positive ​ (a)   and the terminal side lies in Quadrant ​ (b)   . The angles share the same terminal side (and initial side), so they ​ (c)   co-terminal angles. The rotation direction is different: one is positive (​ (d)   ) and the other is negative (​ (e)   ).

• x-axis
• 3
• are
• counterclockwise
• clockwise
• y-axis
• 2
• are not

P4 B.​ (a)   , any angle that shares the ​ (b)   side is co-terminal. So, if you were to rotate ​ (c)   than 1 revolution in the positive or negative direction you ​ (d)   create additional co-terminal angles.

• Yes
• terminal
• could
• more
• No
• initial
• less
• could not

Sketch a pair of co-terminal angles in Quadrant 1.

P4 D-F. The angle with measure 431° is shown. Match the questions with their justification.

• Yes, add or subtract 360^o from the angle

• How could you find a negative co-terminal angle?

• The angle makes more than 1 rotation.

• Is it possible to identify other co-terminal angles?

• Subtract 360^o from 431^o.

• What does the curved arrow tell you about the angle?

• Negative angle with same coterminal side

• How could you find a positive co-terminal angle?

P5 A. The arcs are intercepted by the ​ (a)   central angle. The arcs appear to be ​ (b)   lengths.

• same
• different

P5 B. The length of the arc ​ (a)   as the radius ​ (b)   .

• increases
• decreases

P5 C. The ratio of the number of degrees in the central angle given to the number of degrees in a full circle is ​ (a)   /​ (b)   . This represents ​ (c)   /​ (d)   of circle rotated by the angle.

• 200
• 360
• 5
• 9th
• 5th
• 9

P5 D. The radius of the circle on which arc ABC lies is ​ (a)   . The radius of the circle on which arc DEF lies is ​ (b)   . The radius of the circle on which arc GHI lies is ​ (c)   . So, the calculations represent the circumference of each of the three circles on which the arcs lie ​ (d)   the portion of the ​ (e)   represented by the central angle that forms each of the arcs.

• 1
• 2
• 3
• times
• circumference
• plus
• radius

P4 E. Find the ratio of the arc length to the radius for arc ABC, DEF, and GHI. What do you notice?

• They are the same.

• They are all different.

• They are multiples of each other.

• They are factors of each other.

P6 A. A conversion factor with degrees in the ​ (a)   is used so that the unit of degrees cancels out and the remaining unit is radians; In general, you want to use the conversion factor that cancels out the ​ (b)   unit by having it in the ​ (c)   and the ​ (d)   unit in the ​ (e)   .

• denominator
• existing
• desired
• numerator