radians and angles
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Radians and AnglesWelcome to Trigonometry!!
Starring
The Coterminal Angles
Supp & Comp Angles
The Converter
And introducing…
Angles
Rad Radian
Degree
THE UNIT CIRCLE
1
0.5
-0.5
-1
-2 -1 1 2
You & I are gonna be great
friends!
Angle- formed by rotating a ray about its endpoint (vertex)
Initial Side Starting position
Terminal Side Ending position
Standard PositionInitial 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
Length BC on AB = 4.31 cm
m AB = 4.31 cm
A B
C
Arc length “s” = radius when = 1 radian
Calculate the number of radians in one full circle:
1
0.5
-0.5
-1
-2 -1 1 2
C = r2
r
s
radius
length arc
radians 22 r
r
0
3.14
0, 2
0, 6.28
571.12
712.42
3
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 38036020
34036020
Find 2 coterminal angles to 4
15
4
8
4
15
24
15
4
8
4
15
24
15
4
23
4
8
4
7
Find a negative coterminal angle to 20º
4
Now, you try…
Find two coterminal angles (+ & -) to 3
2
What did you find?
3
8,
3
4
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
6
62
36
2
66
3
3
2
3
233
2
3
3
To convert from degrees radians, multiply by
To convert from radians degrees, multiply by
180
180
Convert to radians:
180
135
4
3
180
80
9
4
To convert from degrees radians, multiply by
To convert from radians degrees, multiply by
180
180
Convert to degrees:
180
3
8 480
180
6
5 150
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 365010as decimal degrees
3660
50
3600
10
8361.3636 + .8333 + .00277
OR Use your calculator!! Express 365010as decimal degrees
Enter 36
Press this button ’ ’’Press enter
Enter 50
Press this button ’ ’’Go over to the ’ symbol -- enter
Enter 10Press this button ’ ’’Go over to the ’’ symbol -- enterPress 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