1. Angles and Their Measure
Objective: Students will be able to find coterminal and reference angles. Students will also be able to find the arc length and area of a sector.
EQ: How do I measure angles and put them in standard position? What are radians and how do they relate to degrees and trigonometry in general?
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3. Standard position: Vertex is at the origin
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4. Finding Coterminal Angles
Two angles with the same initial and terminal sides but
possibly different rotations are called coterminal angles.
Smallest angle made from the terminal side to x-axis is called the reference angle. It is always positive and < 90˚.
Assume the following angles are in standard position. Coterminal and/or reference angle:
a ° angle
b. –135° angle

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6. Convert 40°12’5” to a decimal in degrees
Convert 40°12’5” to a decimal in degrees. Round the answer to four decimal places.
Convert ° to the D°M’S” form. Round the answer to the nearest second.
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9. Definition of a Radian
One radian is the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle.

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11. 360°
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12. (a) 30° (b) 120° (c) – 60° (d) 270° (e) 104 °
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13. Draw and label the angle in standard position.
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16. Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian.
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18. Find the area of the sector of a circle of radius 5 feet formed by an angle of 60˚. Round the answer to two decimal places.
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