2. Radians and Angles Welcome to Trigonometry!! Starring The Coterminal Angles Supp & Comp Angles The Converter And introducing… Angles Rad Radian Degree

3. THE UNIT CIRCLE You & I are gonna be great friends!

4. Angle- formed by rotating a ray about its endpoint (vertex) Initial Side Starting position Terminal SideEnding position Standard Position Initial side on positive x-axis and the vertex is on the origin

5. Angle describes the amount and direction of rotation 120°–210° Positive Angle- rotates counter-clockwise (CCW) Negative Angle- rotates clockwise (CW)

6. 1 Radian = measure of central angle, , that intercepts the arc that has the same length as the radius of the circle Arc length “s” = radius when  = 1 radian

7. Calculate the number of radians in one full circle: C = 0  3.14 0, 2  0, 6.28 Therefore, we can say that 1 full revolution = 2  radians.

8. Coterminal Angles:Two angles with the same initial and terminal sides Find a positive coterminal angle to 20º Find 2 coterminal angles to Find a negative coterminal angle to 20º

9. Now, you try… Find two coterminal angles (+ & -) to What did you find? These are just two possible answers. Remember…there are more!

10. Complementary Angles: Two angles whose sum is 90  Supplementary Angles: Two angles whose sum is 180 

11. To convert from degrees radians, multiply by To convert from radians degrees, multiply by Convert to radians:

12. To convert from degrees radians, multiply by To convert from radians degrees, multiply by Convert to degrees: So, you think you got it now?

13. 1 degree = 60 minutes 1° = 60 1 minute = 60 seconds 1 = 60  So … 1 degree = _________seconds 3600 Express 36  5010  as decimal degrees 36 36 +.8333 +.00277

14. OR Use your calculator!! Express 36  5010  as decimal degrees Enter 36 Press this button  ’ ’’ Press enter Enter 50 Press this button  ’ ’’ Go over to the ’ symbol -- enter Enter 10 Press this button  ’ ’’ Go over to the ’’ symbol -- enter Press enter

15. Convert 50  47’ 50’’ to decimal degree 50.7972 Convert 125  27’ 6’’ to decimal degree 125.4517 Can you go backwards and convert the decimal degree to degrees minutes seconds? Enter 125.4517 Go to DMS hit enter.

16. Express 50.525  in degrees, minutes, seconds 50º +.525(60) 50º + 36.5 50º + 36 +.5(60)  50 degrees, 36 minutes, 30 seconds