convert 105 degrees to radians

convert 105 degrees to radians

The Correct Answer and Explanation is:

To convert 105 degrees to radians, you can use the following formula:Radians=Degrees×π180\text{Radians} = \text{Degrees} \times \frac{\pi}{180}Radians=Degrees×180π​

Here’s the step-by-step process for converting 105 degrees to radians:

1. Write the conversion formula: 105∘×π180∘105^\circ \times \frac{\pi}{180^\circ}105∘×180∘π​
2. Multiply the degrees by π\piπ: 105×π=105π105 \times \pi = 105\pi105×π=105π
3. Divide by 180: 105π180\frac{105\pi}{180}180105π​
4. Simplify the fraction: 105180=712\frac{105}{180} = \frac{7}{12}180105​=127​
5. Final expression in radians: 105∘=7π12 radians105^\circ = \frac{7\pi}{12} \, \text{radians}105∘=127π​radians

So, 105 degrees is equal to 7π12\frac{7\pi}{12}127π​ radians.

Explanation

The reason we convert from degrees to radians is because radians are the standard unit of angular measurement used in mathematics and physics, especially in calculus. The unit circle, which is fundamental to trigonometry, is based on radians. One full rotation (360 degrees) corresponds to 2π2\pi2π radians. This is why the ratio π/180\pi/180π/180 comes into play when converting between the two units.

To understand this better, imagine that a circle has a total angle of 360∘360^\circ360∘. The corresponding angle in radians is 2π2\pi2π radians. This gives us a direct relationship: for every 180 degrees, the angle measures π\piπ radians. This is why we multiply the degree value by π/180\pi/180π/180 to convert it to radians.