Convert the following radians to degrees. Round your answers to one decimal place.

[tex]\[
\begin{array}{l}
\frac{1}{2} \pi = \square \\
-\frac{3}{7} \pi = \square
\end{array}
\][/tex]



Answer :

To convert radians to degrees, we use the formula:

[tex]\[ \text{degrees} = \text{radians} \times \left(\frac{180}{\pi}\right) \][/tex]

Let's apply this formula to the given radian values.

1. For \(\frac{1}{2} \pi\):

- First, we identify the radian value: \(\frac{1}{2} \pi\).
- Now, we multiply this value by \(\frac{180}{\pi}\):

[tex]\[ \frac{1}{2} \pi \times \left(\frac{180}{\pi}\right) = \frac{1}{2} \times 180 \][/tex]

- Simplifying this, we get:

[tex]\[ = 90.0 \][/tex]

Therefore, \(\frac{1}{2} \pi = 90.0\) degrees.

2. For \(-\frac{3}{7} \pi\):

- First, we take the radian value: \(-\frac{3}{7} \pi\).
- Now, we convert this to degrees by multiplying by \(\frac{180}{\pi}\):

[tex]\[ -\frac{3}{7} \pi \times \left(\frac{180}{\pi}\right) = -\frac{3}{7} \times 180 \][/tex]

- Simplifying this, we perform the multiplication:

[tex]\[ = -77.1 \][/tex]

Therefore, \(-\frac{3}{7} \pi = -77.1\) degrees.

Thus, the conversions are:

[tex]\[ \begin{array}{l} \frac{1}{2} \pi = 90.0^\circ \\ -\frac{3}{7} \pi = -77.1^\circ \end{array} \][/tex]