Question

convert the angle 2 radians to degrees, rounding to the nearest 10th.

Explanation:

Step1: Recall the conversion formula

To convert radians to degrees, we use the formula: \(\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}\)

Step2: Substitute the given value

We are given \(2\) radians. Substitute into the formula: \(\text{Degrees} = 2\times\frac{180^\circ}{\pi}\)

Step3: Calculate the value

First, calculate \(2\times180 = 360\), then divide by \(\pi\): \(\frac{360}{\pi}\approx114.591559\)

Step4: Round to the nearest tenth

Rounding \(114.591559\) to the nearest tenth gives \(114.6\)

Answer:

\(114.6\) degrees