Radian Measure. Many things can be measured using different units.

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Presentation transcript:

Radian Measure

Many things can be measured using different units.

Example: Temperature: Fahrenheit and Celsius

Many things can be measured using different units. Example: Temperature: Fahrenheit and Celsius Other Examples?

Angles can be measured with different units too.

- Degrees - Radians:

Angles can be measured with different units too. - Degrees: 1/360 th of a circle - Radians:

Angles can be measured with different units too. - Degrees: 1/360 th of a circle - May be relate to the number of days in a year - Radians:

Angles can be measured with different units too. - Degrees: 1/360 th of a circle - May be relate to the number of days in a year - Radians: ratio between the arc created by the angle and the radius

What is a Radian?

Radian: 1 Radian is the measure of the angle which creates an arc which is the same length as the radius.

What is a Radian? Radian: 1 Radian is the measure of the angle which creates an arc which is the same length as the radius.

Radians are typically reported in terms of π.

- There are 2π radians in one full rotation around a circle

You have used Radians before!!

Formula for circumference of a circle:

You have used Radians before!! Formula for circumference of a circle: C = 2πr

You have used Radians before!! Formula for circumference of a circle: C = 2πr Formula for area of a circle:

You have used Radians before!! Formula for circumference of a circle: C = 2πr Formula for area of a circle: A = πr 2

Converting from degrees to radians: Formula: Radians = Degrees ∙

Converting from degrees to radians: Formula: Radians = Degrees ∙ * Typically leave answer as a fraction in reduced form.

Convert to Radians: 30°

Convert to Radians: 90°

Convert to Radians: 400°

Convert to Radians: –45°

Convert to Radians: 120°

Convert to Radians: 225°

Converting from Radians to Degrees: Formula: Degrees = Radians ∙

Convert from Radians to Degrees: