Dorchester2-03-13-2025 Degree to Radian Measure

By Antoinette Norris Woodson

Draw

If a dog is worth 5, what are the other animals worth?

be prepared to explain your reasoning.

Explanation Slide...

Draw

FINISH at the square with a star in it.

Find the START point on the grid.

DRAW your path.

● I can define the parts of a circle
● I can define and measure in a circle
● I can find the measure of segments of a circle
● I can discover the properties of tangent lines
● I can find the measure of angles inside and outside of a circle
● I can find missing measures of angles and arcs using circle theorems.

● I can explain radian angle measures in terms of a circular radius and
arc length

Objectives

Vocabulary

Degree- Standard System measure of an angle from its initial side to final side. The measure around the unit circle is 0°-360°, where 360° is a full rotation.

Draw

Draw the following.

Draw the x- and y- axis.

Draw three units in each quadrant (leave lots of space)

Draw a circle with a radius one and the center at (0,0).

Label the coordinates where the circle intersects each axis.

Find the circumference of the circle.

Show all steps of the process.

We know that a circle is 360 degrees

How about measuring it in radians?

Match

Match the following

90 Degrees

-270 Degrees

250 Degrees

-110 Degrees

270 Degrees

• 90 Degrees

• -270 Degrees

• 250 Degrees

• -110 Degrees

• 270 Degrees

Converting Radians to degrees

Converting Hints

• If you convert from Degrees, pi will show up in your answer for radians....

• Leave Pi as a symbol in radians! (unless you need a decimal answer)

• If you converting from Radians, pi will cancel out

Converting 200 degrees to radians

​Converting Radians to Degrees

Converting from degrees to radians

Multiple Choice

Which of the following is closest to the measure of the angle shown?

• 30º

• 40º

• 395º

• 440º

Converting 200 degrees to radians

​Converting Radians to Degrees

Multiple Choice

What is  $$225\degree$$   in radians? 

• $$\frac{7\pi}{4}$$  

• $$\frac{5\pi}{4}$$  

• $$\frac{3\pi}{4}$$  

• $$\frac{5\pi}{3}$$  

Multiple Choice

What is $$270\degree$$  in radians?

• $$\frac{\pi}{4}$$

• $$\frac{3\pi}{2}$$

• $$\frac{3\pi}{4}$$

• $$\frac{\pi}{2}$$

Multiple Choice

Convert 150⁰ to radians

• $$\frac{5\pi}{6}$$

• $$\frac{3\pi}{4}$$

• $$\frac{7\pi}{6}$$

• $$\frac{2\pi}{3}$$

Multiple Choice

Convert 510^o to Radians

• 25π / 3

• 23π / 8

• 17π / 6

• 51π / 8

Multiple Choice

How many RADIANS are in a circle?

• 180^o

• 360^o

• π rad

• 2π rad

Fill in the Blanks

$\frac{\pi}{4}$   radians =

degrees

Poll

What is your level of confidence of today's lesson?