What professionals might use radians? Any engineer or scientist who deals with electricity,

someone who works with electronic music, automotive engineers, electronic circuit designers,

and my favorite, mathematicians.

• Locate the center of a circle by balancing the circle on the tip of a pencil.

• Mark the length of the radius of the circle on an index card. Cut the card the length of the radius

• Create a radius wedge (a pie-shaped piece formed by two radii and an arc length of 1 radius)

• Measure the angle in degrees. 1 radian is approximately _______ degrees.

• Continue marking full radians around the circle. Approximately how many radians are there in a full circle? _______

How many in a half circle? _______

• The formula for the circumference of a circle is _____________. The radius of our circle is one, so the number of radians in a 360˚ circle is _________.

• The number of radians in a semicircle (180˚) is _____________.

• The number of radians in a quarter circle is (90˚) is ______________.

• The number of radians in an eighth circle is (45˚) is ______________.

So What is a Radian, Really?So What is a Radian, Really?

RadianRadianA more convenient method for measuring angles (instead of degrees) in upper level mathematical applications.

The radian measure of an angle in standard position is defined as the length of the corresponding arc on the unit circle.

The measure of is “s” radians.

Convert 48.555º to degrees, minutes, seconds:Type 48.555 ►DMS                        

Answer:  48º 33' 18''        

The ►DMS is #4 on the Angle menu (2nd APPS).  This function works even if Mode is set to Radian.

FYI (On the Calculator):FYI (On the Calculator):

Degrees to radians: multiply by π/180

Radians to degrees: multiply by 180/π

It will be helpful to memorize these common angle measures and their equivalent radian measures:

6

11

180

330

180330

1203

360180

3

2

60 is angle reference

the;240 toscorrespond 34

60°

1

- 1/2

2

3

r

xcos 2

121

34

1cos

Remember “The Chart”

240˚ is in Quadrant III, so the sign is . . . All Students Take Calculus

. . . negative

2

1

3

4 cos

60 cos

OR

2

1

Sector – the region bounded by a central angle Sector – the region bounded by a central angle and its intercepted arcand its intercepted arc

Example 6Example 6

HW: Page 348HW: Page 348