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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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**Angles**Rad Radian Degree Radians and Angles Welcome toTrigonometry!! 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 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**120°**–210° Angle describes the amount and direction of rotation Positive Angle- rotates counter-clockwise (CCW) Negative Angle- rotates clockwise (CW)**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**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.**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**Now, you try…**Find two coterminal angles (+ & -) to What did you find? These are just two possible answers. Remember…there are more! **Complementary Angles: Two angles whose sum is 90**Supplementary Angles: Two angles whose sum is 180**To convert from degrees radians, multiply by**To convert from radians degrees, multiply by Convert to radians:**To convert from degrees radians, multiply by**To convert from radians degrees, multiply by So, you think you got it now? Convert to degrees:**1 degree = 60 minutes**1° = 60 1 minute = 60 seconds 1 = 60 3600 So … 1 degree = _________seconds Express 365010as decimal degrees 36 36 + .8333 + .00277**OR**Express 365010as 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**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.**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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