Angles, Radians, and Arc Length

Explore degree-radian conversion, coterminal angles, arc length.

Lesson 1 of 53 parts Practice Flashcards

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Degree-Radian Conversion

Objective: Explain degree-radian conversion and use it to solve or interpret a problem.

A full rotation is 360°=2π radians; multiply degrees by π/180 or radians by 180/π. State the unit with the result. Yes.

Worked examples

Try itAngles, Radians, and Arc Length — practice 1.1: Convert 150° to radians. Give the coefficient of π.Show answer

Step 1: Multiply 150° by π/180°. Step 2: Reduce 150/180. Step 3: The radian measure is 5/6π.

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Degree-Radian Conversion

Objective: Explain degree-radian conversion and use it to solve or interpret a problem.

A full rotation is 360°=2π radians; multiply degrees by π/180 or radians by 180/π. State the unit with the result. Yes.

Worked examples

Try itAngles, Radians, and Arc Length — practice 1.1: Convert 150° to radians. Give the coefficient of π.Show answer

Step 1: Multiply 150° by π/180°. Step 2: Reduce 150/180. Step 3: The radian measure is 5/6π.

Coterminal Angles

Objective: Explain coterminal angles and use it to solve or interpret a problem.

Angles differing by an integer multiple of 2π radians have the same terminal side. A reference angle measures an acute angle to the x-axis. Add 2π repeatedly to a radian angle.

Worked examples

Try itAngles, Radians, and Arc Length — practice 2.1: Convert 240° to radians. Give the coefficient of π.Show answer

Step 1: Multiply 240° by π/180°. Step 2: Reduce 240/180. Step 3: The radian measure is 4/3π.

Arc Length

Objective: Explain arc length and use it to solve or interpret a problem.

For radius r and central angle θ in radians, arc length s=rθ. Converting degrees first prevents a factor error. Radians, not degrees.

Worked examples

Try itAngles, Radians, and Arc Length — practice 3.1: An angle of π/3 radians cuts a circle of radius 33. Find arc length as a coefficient of π.Show answer

Step 1: Use arc length s=rθ with θ in radians. Step 2: Multiply 33·(π/3). Step 3: The length is 11π; coefficient 11.

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