(1^\circ) is approximately equal to how many radians?

Correct answer: (0.01745) radian

The direct answer is option A: \(1^\circ\approx0.01745\) radians. Since 180° equals \(\pi\) radians, divide both sides by 180: \(1^\circ=\frac{\pi}{180}\) radians. With \(\pi\approx3.1416\), \(\frac{3.1416}{180}\approx0.01745\). Option A has exactly this value. Option B, 0.1745, is ten times too large and is close to 10° in radians. Option C, 1.745, is about 100° in radians, so it is far too large. Option D, 17.45, is also much too large and cannot represent a one-degree angle. A useful size check is that one degree is a very small angle, so its radian measure must be much less than 1. Remember: degree to radian means multiply by \(\frac{\pi}{180}\).