#### Transcript 13-2 General Angles and Radian Measure

**13-2 General Angles and Radian Measure**

**What is pi?**

**A delicious dessert? Yes, but not quite… Def: The ratio of a circle’s circumference to it’s diameter.**

**What is a radian?**

**Def: Standard unit of angle measure, equal to the arc length of the corresponding angle on the unit circle.**

**What is the Unit Circle you ask??**

**It’s just what it sounds like, the Unit Circle is a circle that has a radius of One Unit. The Unit Circle gives us some very important principles in Trigonometry.**

**What is a radian?**

**We always start with an angle created from the x-axis-also called the standard position.**

**The ending position (or terminal side) of the angle gives us the radian measure.**

θ

**r How to convert from degrees to radians:**

deg

*ree*

180

*radians*

**Standard position**

**Ex 1: Convert 120° to radians**

deg

*ree*

180

*radians*

120 180

*radians*

π( 2 2 3 3 ) (

*radians*

*radians*

)π

deg

*ree*

180 deg 180

**Ex 2: Convert to degrees**

4

*rees radians*

4 180( deg deg

*rees*

180

*rees*

) ( )180 45 4 deg

*rees*

180 4 1

**Arc Length and Area of a Sector**

**Arc Length:**

*s*

*r*

1

**Area of Sector:**

2

*r*

2

**(θ is in radians) θ r Arc Length (s)**

**Surface Area = Area of the sector**

**Ex 3: You cut yourself a slice of pie, from an apple pie that has a radius of 3 in. The slice that you cut has a central angle of 60°. What is the surface area of the pie you are about to consume? How much crust are you eating?**

1 2

**Crust = Arc Length**

*s*

*r*

2

*r*

1 2 3 2 ( 3 ( 3 ) 3 ) 3 2 r= 3 θ 3

**So…What does the a radian LOOK like?**

**A circle has 360°, how many radians is that?**

360 180

*radians*

π( ) (

*radians*

2

*radians*

)π

**If 360° is 2π, then how many radians is 180° do you suppose?**

2

**To find the rest of the angles, we simply “slice” up the pi… Ex 4: Draw an angle with the given measure in standard position.**

3 4 3 2

**Ex 5: Draw an angle with **

4

**the given measure in **

**standard position.**

2 3 2 3 2

**810° Ex 6: Draw an angle with the given measure in standard position.**

**This is obviously larger then 360°, so what will this angle look like?**

**810° 810°-720°=90°**

2

**Did you notice that 810° looked a lot like 90°? We call these angles Coterminal angles, because their terminal sides (ending sides) coincide.**

**What are some other coterminal angles of 90°?**

**Terminal Side 90°/810°**

**Are there negative coterminal angles of 90°?**

2