What is 45 degrees converted to radians?

What is 45 degrees converted to radians?

• A. π/2
• B. π/4
• C. π/3
• D. π

Answer: (B)

To convert degrees to radians, the relationship between these two measurements is crucial to understand. One complete revolution (360 degrees) is equivalent to \(2\pi\) radians. Therefore, to convert degrees to radians, you can use the formula: \[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \] For the angle given in the question, which is 45 degrees, you would apply this formula: \[ \text{radians} = 45 \times \frac{\pi}{180} \] Simplifying this expression involves reducing the fraction: \[ \frac{45}{180} = \frac{1}{4} \] Thus, the calculation becomes: \[ \text{radians} = \frac{1}{4} \pi = \frac{\pi}{4} \] This value, \(\frac{\pi}{4}\), is the correct conversion of 45 degrees into radians. The significance of this conversion lies in its utility in trigonometric calculations and ensuring that angles are appropriately expressed for the mathematical functions which operate in radian measure.

To convert degrees to radians, the relationship between these two measurements is crucial to understand. One complete revolution (360 degrees) is equivalent to (2\pi) radians. Therefore, to convert degrees to radians, you can use the formula:

[

\text{radians} = \text{degrees} \times \frac{\pi}{180}

]

For the angle given in the question, which is 45 degrees, you would apply this formula:

[

\text{radians} = 45 \times \frac{\pi}{180}

]

Simplifying this expression involves reducing the fraction:

[

\frac{45}{180} = \frac{1}{4}

]

Thus, the calculation becomes:

[

\text{radians} = \frac{1}{4} \pi = \frac{\pi}{4}

]

This value, (\frac{\pi}{4}), is the correct conversion of 45 degrees into radians. The significance of this conversion lies in its utility in trigonometric calculations and ensuring that angles are appropriately expressed for the mathematical functions which operate in radian measure.