Convert 7.26 radians to degrees. Give your answer to 2 decimal places.
Understand the Problem
The question is asking us to convert an angle measured in radians (7.26) into degrees. The conversion can be done using the formula: degrees = radians × (180/π). We will calculate the equivalent degrees and round the answer to two decimal places.
Answer
The angle in degrees is approximately $416.03$.
Answer for screen readers
The angle in degrees is approximately $416.03$ degrees.
Steps to Solve
- Identify the given value in radians
We are given the angle in radians, which is $7.26$ radians.
- Use the conversion formula
We apply the conversion formula to convert radians to degrees:
$$ \text{degrees} = \text{radians} \times \left( \frac{180}{\pi} \right) $$
Inserting the value of radians:
$$ \text{degrees} = 7.26 \times \left( \frac{180}{\pi} \right) $$
- Calculate the value
Now, we can perform the calculation using the approximation for $\pi \approx 3.14159$:
$$ \text{degrees} = 7.26 \times \left( \frac{180}{3.14159} \right) $$
Calculating this gives:
$$ \text{degrees} \approx 7.26 \times 57.2958 \approx 416.027 $$
- Round the result
Finally, round the result to two decimal places:
$$ \text{degrees} \approx 416.03 $$
The angle in degrees is approximately $416.03$ degrees.
More Information
When converting from radians to degrees, the relation between them is crucial. This method of conversion is widely used in trigonometry, physics, and engineering.
Tips
- Forgetting to multiply by $\frac{180}{\pi}$: It's essential to use this entire factor for proper conversion.
- Not rounding the final answer: Always round to the specified number of decimal places as required.
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