Converting Degrees/Radians
Radians and degrees are two units for measuring angles. There are at
least four such units, but degrees and radians are the ones you are most
likely to encounter in high school and college
Degrees-a unit of measurement of angles, one three-hundred-and-sixtieth of the
circumference of a circle
Radians-a unit of angle, equal to an angle at the center of a circle whose arc is
equal in length to the radius
FORMULA: degrees= radians x 180/n
Radians= degrees x n/180
Examples Problems:
1. Convert 200° into radian measure:
200∘·π/180∘
=10/π9radians =3.49 radians
2. Convert 1.4 radians into degrees:
1.4·180∘/π
=252∘/π ≈80.2
EXPLANATION:
When converting degrees to radians, you must find the equivalent angle;
formula is needed
When converting radians to degrees, the formula is needed.
Practice Problems: GRAB YOUR CALCULATION
Choose:
-288º
Convert
to degrees.
-124º
-72
Co-terminal/Reference angles
Convert 135º to radian measure.
Choose:
Co-terminal/Reference Angles
Co-terminal angles are angles in standard position (angles
with the initial side on the positive x-axis) that have a
common terminal side. For example 30°, –330° and 390°
are all co-terminal.
Reference angle is the smallest angle between the
terminal side and the x-axis. The values of the trig
functions of angle θ are the same as the trig values of
the reference angle for θ, give or take a minus sign
Example Problems:
Find a positive and a negative angle coterminal with a 55°
angle.
55° – 360° = –305°
55° + 360° = 415°
A –305° angle and a 415° angle are coterminal with a 55°
angle.
Example 2:
Find a positive and a negative angle coterminal with a
angle.
A
angle and a
Example Problem:
180o
Step-By-Step Solution:
Since the angle
angle are coterminal with a
angle.
180°is in the second quadrant, the reference angle formula is
Ar=180°−Ac.
Ar=180°−A
Substitute180°for A in the equation Ar=180°−Ac.
Ar=180°−180°
The reference angle is Ar=0°
Practice Problems:
What is the reference angle for a 210° angle?
SHOW ANSWER
Find a positive and negative coterminal angle for 10 degrees.
SHOW ANSWER
SOLUTIONS
Degrees and Radians: Both answers are C
Coterminal and Reference: 30 degress is the first
answer. The second answer is First add 360 to 10 to get
your positive coterminal angle
10+360= 370 degrees
Then subtract 360 from 10 to get your negative
coterminal angle.
10-360= -350 degrees
IF YOU NEED FURTHER HELP
https://www.youtube.com/watch?v=dz5Y
pNFuhRQ
https://www.youtube.com/watch?v=qgGF
QXnuszk
https://www.youtube.com/watch?v=aci0c
0dtzGg