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Radians and Angles

Angles Rad Radian Degree. Radians and Angles. Welcome to Trigonometry!!. Starring. The Coterminal Angles Supp & Comp Angles The Converter. And introducing…. THE UNIT CIRCLE. You & I are gonna be great friends!. Angle-. Terminal Side. Initial Side.

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Radians and Angles

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  1. Angles Rad Radian Degree Radians and Angles Welcome toTrigonometry!! Starring The Coterminal Angles Supp & Comp Angles The Converter And introducing…

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

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

  4. 120° –210° Angle describes the amount and direction of rotation Positive Angle- rotates counter-clockwise (CCW) Negative Angle- rotates clockwise (CW)

  5. 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

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

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

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

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

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

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

  12. 1 degree = 60 minutes 1° = 60  1 minute = 60 seconds 1  = 60  3600 So … 1 degree = _________seconds Express 365010as decimal degrees 36 36 + .8333 + .00277

  13. OR Express 365010as decimal degrees Use your calculator!! 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

  14. 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.

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

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