Convert 65 degrees to radians.
Understand the Problem
The question is asking to convert an angle measured in degrees (65 degrees) into radians. This can be done using the conversion factor that π radians is equal to 180 degrees.
Answer
$ \frac{13\pi}{36} $
Answer for screen readers
The angle $65$ degrees is equivalent to $\frac{13\pi}{36}$ radians.
Steps to Solve
- Identify the conversion relationship
We know that $180$ degrees is equivalent to $\pi$ radians. We will use this relationship to convert $65$ degrees into radians.
- Set up the conversion equation
To convert degrees to radians, we use the formula: $$ \text{radians} = \text{degrees} \times \frac{\pi \text{ radians}}{180 \text{ degrees}} $$
- Substitute the values
Now we substitute the value of degrees into the equation: $$ \text{radians} = 65 \times \frac{\pi}{180} $$
- Calculate the radians
To compute the radians, we first simplify the fraction: $$ \text{radians} = \frac{65\pi}{180} $$ Next, we can simplify $\frac{65}{180}$ to $\frac{13}{36}$: $$ \text{radians} = \frac{13\pi}{36} $$
The angle $65$ degrees is equivalent to $\frac{13\pi}{36}$ radians.
More Information
Converting angles from degrees to radians is essential in trigonometry, as many mathematical functions require angles to be in radians. Additionally, this conversion is widely used in physics and engineering.
Tips
- Forgetting to use π in the conversion or misplacing it when simplifying.
- Incorrectly simplifying the fraction, which can lead to inaccurate results.
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