Digital SATMath: Geometry and TrigonometryHard
A student is using a protractor to measure an angle in radians. If the angle measures 120°, what is this angle in radians?
- A3π/2 radians
- Bπ/2 radians
- Cπ/3 radians
- D2π/3 radians
Show answer & explanationAnswer & explanation
Correct answer: D. 2π/3 radians
To convert degrees to radians, use the conversion factor (π radians / 180°). So, 120° * (π radians / 180°) = 120π/180 radians. Simplifying the fraction 120/180: divide both by 60 to get 2/3. Therefore, 120° = 2π/3 radians.
Why the other options are wrong
- A. This is 270° in radians, not 120°.
- B. This is 90° in radians, not 120°.
- C. This is 60° in radians, not 120°.
Degrees to Radians Conversion
The process of changing an angle's measurement from degrees to radians.
- Conversion factor: π radians = 180°.
- Multiply degrees by (π/180) to get radians.
- Radians are a unit of angular measurement based on the radius of a circle.
Memory trick: Degrees to Radians: 'Pi over 180' is your conversion key.