Convert between Radians and Degrees
Radians and degrees are two different units used to measure angles. Understanding how to convert between them is essential for solving many trigonometric problems. The entire process is based on the relationship between a full revolution in both units:
\(360^\circ = 2\pi \text{ radians}\)
This simplifies to the important conversion factor:
\(180^\circ = \pi \text{ radians}\)
 
In this game, you will need to convert between radians and degrees. There are three modes: Degrees to Radians, Radians to Degrees, and Mixed Challenge. It includes a scoring system, and clear feedback to help you master this skill.
 

Angle Converter Challenge

Score: 0 Question: 0

Select Mode to Start

Next Angle ➜ ← Back to Mode Selection

Choose your conversion challenge:

Degrees $\to$ Radians Radians $\to$ Degrees Mixed Challenge

 

How to Play the Convert Radians and Degrees Game
The game will show you a function. Your task is to differentiate the exponential or log function and select the correct answer.
Here’s how to play:

1. Start: Each Quiz consists of 10 questions. Click “Start Game”.
   
2. Look at the Problem: You will be given a function.
   
3. Select Your Answer: Select the correct derivative.br>
4. Check Your Work: Click “Submit Selection”. The game will tell you if you’re correct. If you are wrong, the correct answer will be highlighted in green.
   
5. Get a New Problem: Click “Next Question” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
6. Finish Game When you have completed 10 questions, click “Finish Game” to get your final score.
    
   

Radian and Degree Conversion
Radians and degrees are two different units used to measure angles. Understanding how to convert between them is essential for solving many trigonometric problems.
The process is based on the relationship between a full revolution in both units:
\(360^\circ = 2\pi \text{ radians}\)
This simplifies to the conversion factor:
\(180^\circ = \pi \text{ radians}\)

1. Degrees to Radians
To convert an angle from degrees to radians, you need to multiply the degree measure by the conversion factor \(\left(\frac{\pi}{180^\circ}\right)\). This ensures the degree units cancel out, leaving the angle in radians (often left in terms of \(\pi\)).
\(\text{Radians} = \text{Degrees} \times \frac{\pi}{180^\circ}\)

Example: Convert \(60^\circ\) to radians
Set up the equation:
\(\text{Radians} = 60^\circ \times \frac{\pi}{180^\circ}\)
Simplify the fraction:
\(\text{Radians} = \frac{60\pi}{180}\)
Reduce the fraction to its lowest terms (divide the numerator and denominator by 60):
\(\text{Radians} = \frac{1\pi}{3} = \frac{\pi}{3}\)
Therefore, \(60^\circ\) is equal to \(\frac{\pi}{3}\) radians.

2. Radians to Degrees To convert an angle from radians to degrees, you use the reciprocal of the first conversion factor, \(\left(\frac{180^\circ}{\pi}\right)\). This ensures the $\pi$ (radian unit) cancels out, leaving the angle in degrees.
\(\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}\)

Example: Convert \(\frac{3\pi}{4}\) radians to degrees
Set up the equation:
\(\text{Degrees} = \frac{3\pi}{4} \times \frac{180^\circ}{\pi}\)
Cancel out \(\pi\) and simplify:
\(\text{Degrees} = \frac{3}{4} \times 180^\circ\)
Perform the multiplication:
\(\text{Degrees} = 3 \times (180 \div 4)^\circ\)
\(\text{Degrees} = 3 \times 45^\circ\)
\(\text{Degrees} = 135^\circ\)
Therefore, \(\frac{3\pi}{4}\) radians is equal to \(135^\circ\).
 

This video gives a clear, step-by-step approach to learn how to convert between radians and degrees.

• Show Video

 

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