5.1 Standard Form of Angles, Radians, and Degrees

Unit 5: Trigonometry

5.1 Standard Form of Angles, Radians, and Degrees

1. Vocabulary:

1. Standard Form of Angles- an angle is in standard form when the vertex is on the origin and one ray lies on the positive x-axis.

1.Vocabulary

2. 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.

1.Vocabulary

3. Radians- Metric System measure of an angle from its initial side to final side. The measure around the unit circle is 0-2π, where 2π is a full rotation.

Any angle measure greater than 2 π or 360° means that the angle has gone completely around the circle at least once.

Match

Match the following

90 Degrees

-270 Degrees

250 Degrees

-110 Degrees

270 Degrees

• 90 Degrees

• -270 Degrees

• 250 Degrees

• -110 Degrees

• 270 Degrees

Multiple Choice

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

• 30º

• 40º

• 395º

• 440º

2. Converting from degrees to radians

1. Convert from degree to radian:

Examples

2. Convert from radian to degree:

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 DEGREES are in a circle?

• 180^o

• 360^o

• π rad

• 2π rad

Multiple Choice

How many RADIANS are in a circle?

• 180^o

• 360^o

• π rad

• 2π rad

Dropdown

$$\pi$$ radians equals ​

Select answer

degrees