Convert 345 degrees to radians.
Understand the Problem
The question is asking how to convert an angle of 345 degrees into radians. This involves using the conversion factor that states 1 degree equals π/180 radians.
Answer
The angle of 345 degrees in radians is $\frac{23\pi}{12}$.
Answer for screen readers
The angle of 345 degrees in radians is $\frac{23\pi}{12}$.
Steps to Solve
- Identify the conversion factor
To convert degrees to radians, we use the conversion factor: $$ \text{Radians} = \text{Degrees} \times \frac{\pi}{180} $$
- Substitute the given angle into the formula
Insert the angle of 345 degrees into the conversion formula: $$ \text{Radians} = 345 \times \frac{\pi}{180} $$
- Simplify the expression
Now, simplify the expression to find the radian measure: $$ \text{Radians} = \frac{345\pi}{180} $$
- Simplify the fraction
To simplify $\frac{345}{180}$, we find the greatest common divisor (GCD) of 345 and 180, which is 15. Now, divide both the numerator and the denominator by 15: $$ \frac{345 \div 15}{180 \div 15} = \frac{23}{12} $$
- Final answer in radians
Now the conversion is complete, so we get: $$ \text{Radians} = \frac{23\pi}{12} $$
The angle of 345 degrees in radians is $\frac{23\pi}{12}$.
More Information
Converting angles between degrees and radians is essential in trigonometry and calculus. Radians are often preferred in calculus because they simplify the computation of derivatives and integrals involving trigonometric functions.
Tips
- Forgetting to use the conversion factor: Always use the correct conversion factor of $\frac{\pi}{180}$ to convert degrees to radians.
- Not simplifying the fraction: Ensure you simplify the fraction for a cleaner final answer.
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