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

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Presentation transcript:

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

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

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

Angle describes the amount and direction of rotation 120°–210° 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 = 0  , 2  0, 6.28 Therefore, we can say that 1 full revolution = 2  radians.

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

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 Convert to degrees: So, you think you got it now?

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

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

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

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