Convert the following degree measure to radians. 135 degrees 10 prime
The correct answer and explanation is:
Correct Answer:
135 degrees 10 minutes = 2.36 radians (rounded to two decimal places)
Explanation:
To convert an angle from degrees and minutes to radians, follow these steps:
Step 1: Convert minutes to decimal degrees.
There are 60 minutes in one degree. So:
10 minutes = 10 ÷ 60 = 0.1667 degrees
Now add this to the degrees:
135 degrees + 0.1667 degrees = 135.1667 degrees
Step 2: Convert degrees to radians.
To convert degrees to radians, use the formula:
Radians = Degrees × (π / 180)
So:
135.1667 × (π / 180) ≈ 135.1667 × 0.0174533 ≈ 2.3581 radians
Rounded to two decimal places, the final result is:
2.36 radians
Why this is important:
Angles can be measured in both degrees and radians. Degrees are common in geometry and everyday contexts, while radians are used more often in calculus, physics, and higher-level mathematics because of their natural relationship to the circle.
Radians are based on the radius of a circle. One full circle is 2π radians, which equals 360 degrees. This means 1 degree equals π/180 radians. So any angle in degrees can be converted by multiplying it with π/180.
The “minutes” in angle measurement are just a finer subdivision of degrees, just like minutes are subdivisions of hours. Converting them to decimal form first simplifies the entire calculation and ensures accurate conversion.
Understanding how to convert degrees and minutes to radians is essential for solving trigonometric equations, working with rotational motion in physics, and analyzing periodic functions in engineering and science.