Academy Algebra II/Trig

1. Academy Algebra II/Trig Pre-Calculus (4.1) 7.1: Angles and Their Measure HW tonight: p.513 (11-22 all) HW tomorrow: p.513 (24-62 even)

2. Angles • The initial side of an angle coincides with the positive x-axis. • Positive angles are generated by a counterclockwise rotation and a negative angleby a clockwise rotation.

3. Coterminal Angles • Angles with the same initial and terminal sides are coterminal angles. Alpha and beta are coterminal angles.

4. Radian Measure • One radian is the measure of a central angle that intercepts an arc s equal in length to the radius r of the circle.

5. Radian Measure • Because the circumference of the circle is , it follows that a central angle of one full revolution corresponds to an arc length of . Therefore, radians corresponds to .

6. Radian Measure Identify the Following angles: 0, , , and . • Other common angles:

7. Determine the quadrant in which the angle lies. (The angle is given in radian measure.) 1.) 2.) 3.) -1 4.) 5.63 5.) 6.)

8. Sketch the angle in standard position. Determine two coterminal angles in radian measure (one positive & one negative) for the given angle. 1.) 2.)

9. Sketch the angle in standard position. Determine two coterminal angles in radian measure (one positive & one negative) for the given angle. 3.) 4.)

10. Determine the quadrant in which the angle lies. 1.) 2.) 3.) 4.)

11. Sketch the angle in standard position. Determine two coterminal angles in degree measure (one positive & one negative) for the given angle. 1.) 2.)

12. Find (if possible) the complement and supplement of the angle. • Two positive angles are complementary if their sum is . Two positive angles are supplementary if their sum is . 1.) 2.) 3.) 3 4.) 1.5

13. Find (if possible) the complement and supplement of the angle. 1.) 2.) 3.) 4.)

14. Do Now: Sketch the angle in standard position. Determine two coterminal angles in degree measure (one positive & one negative) for the given angle. 1.) 2.)

15. Convert degrees to radians

16. Express the angle in radian measure as a multiple of pi. 1.) 2.) 3.) 4.)

17. Convert the angle measure from degrees to radians. Round your answer to three decimal places. 1.) 2.)

18. Express the angle in degrees. 1.) 2.) 3.) 4.)

19. Convert the angle measure from radians to degrees. Round your answer to three decimal places. 1.) 2.) 4.8

20. Convert the angle to decimal form. • 60 minutes = 1 degree • 60 seconds = 1 minute 1.) 2.) 3.)

21. Convert the angle to form. • 60 minutes = 1 degree • 60 seconds = 1 minute 1.) 2.)

22. Do Now: Round your answers to three decimal places. Convert the angle measure from degrees to radians. 1.) 2.) 3.) 4.) -0.48 Convert the angle measure from radians to degrees.

23. Convert the angle to form. • 60 minutes = 1 degree • 60 seconds = 1 minute 3.) 4.)

24. Arc Length

25. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. 1.) r = 22 feet, s = 10 feet 2.) r = 80 km, s = 160 km

26. Find the length of the arc on a circle of radius r intercepted by a central angle of . 1.) r = 9 feet, 2.) r = 40 cm,