Warm-Up: If , find tan θ.

4.2 – Degrees & Radians Objectives: You should be able to convert degrees to radians & vice versa as well as use angle measures to solve real-world problems.

Angles & Their Measures

Radian Measure:

Degree/Radian Conversions:

Example 2:  

Coterminal Angles:  

Example 3: a. Identify all angles that are coterminal with 80°. Then find specifically one positive and one negative coterminal angle. b. Identify all angles that are coterminal with . Then find specifically one positive and one negative coterminal angle.

Arc Length:

Example 4: Find the length of the intercepted arc in a circle with a central angle measure and radius given. Round to nearest tenth if necessary a. Central angle: Radius: 4 in b. Central angle: 125° Radius: 7 cm

 

Example 5: RECORDS A typical vinyl record has a diameter of 30 cm. When played on a turn table, the record spins at revolutions per minute. a. Find the angular speed, in radians per minute, of a record as it plays. Round to the nearest tenth.

Example 5: RECORDS A typical vinyl record has a diameter of 30 cm. When played on a turn table, the record spins at revolutions per minute. b. Find the linear speed at the outer edge of the record as it spins, in centimeters per second.

Area of a Sector:

Example 6: Find the area of the sector of the circle. a. b.