Convert 8 radians to degrees.
Understand the Problem
The question is asking how to convert 8 radians into degrees. To solve this, we will use the conversion factor where 1 radian is equal to 180/π degrees.
Answer
$458.37$ degrees
Answer for screen readers
The final answer is approximately $458.37$ degrees.
Steps to Solve
- Identify the conversion factor
We know that $1$ radian is equal to $\frac{180}{\pi}$ degrees. To convert radians to degrees, we can use this factor.
- Set up the conversion equation
To convert $8$ radians to degrees, we multiply $8$ by the conversion factor:
$$ \text{Degrees} = 8 \text{ radians} \times \frac{180}{\pi} $$
- Calculate the degrees
Now, we compute the value:
$$ \text{Degrees} = 8 \times \frac{180}{\pi} $$
- Evaluate the expression
Using the approximate value of $\pi \approx 3.14$, we can substitute in and calculate:
$$ \text{Degrees} \approx 8 \times \frac{180}{3.14} $$
- Final calculation
Perform the multiplication and division:
$$ \text{Degrees} \approx 8 \times 57.2958 \approx 458.3664 $$
So, $8$ radians is approximately $458.37$ degrees.
The final answer is approximately $458.37$ degrees.
More Information
Converting between radians and degrees is a common task in trigonometry and is useful in various applications, such as physics and engineering. Understanding these conversions can help you visualize angles in different contexts.
Tips
- Forgetting to use the conversion factor of $\frac{180}{\pi}$ correctly. Ensure that radians are multiplied by this factor to convert accurately.
- Miscalculating the value of $\pi$. It's helpful to have an accurate value of $\pi$ during calculations.
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