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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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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