Convert 7 radians to degrees.
Understand the Problem
The question is asking to convert 7 radians into degrees. To solve this, we will use the conversion factor that defines the relationship between radians and degrees.
Answer
Approximately $401.061$ degrees.
Answer for screen readers
The final answer is approximately $401.061$ degrees.
Steps to Solve
- Identify the conversion factor
To convert from radians to degrees, we use the conversion factor that states $180$ degrees is equal to $\pi$ radians. This can be expressed as:
$$ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} $$
- Set up the equation
To convert $7$ radians to degrees, we can multiply by the conversion factor:
$$ \text{Degrees} = 7 \text{ radians} \times \frac{180}{\pi} $$
- Calculate the value
Now we can calculate the value:
$$ \text{Degrees} = 7 \times \frac{180}{\pi} $$
- Use a calculator
Using a calculator, first compute $\frac{180}{\pi} \approx 57.2958$, then multiply by $7$:
$$ \text{Degrees} \approx 7 \times 57.2958 $$
- Final answer
The final calculation gives us:
$$ \text{Degrees} \approx 401.061 $$
The final answer is approximately $401.061$ degrees.
More Information
When converting between radians and degrees, this conversion factor is essential. Knowing that there are approximately $57.2958$ degrees in one radian can help in various applications in trigonometry and geometry.
Tips
- Using incorrect conversion factor: Some might forget that $180$ degrees equals $\pi$ radians and might incorrectly set up the equation.
- Rounding too early: It's best to keep as many decimal places as possible until the final calculation to ensure accuracy.
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