Convert each degree measure to radians. Leave answers as multiples of π .


45°

Verified step by step guidance

1. Convert the degree measure to radians using the formula: radians = degrees \times \frac{\pi}{180}
2. Substitute 45 for degrees in the formula: radians = 45 \times \frac{\pi}{180}
3. Simplify the fraction: \frac{45}{180} = \frac{1}{4}
4. Multiply the simplified fraction by \pi: \frac{1}{4} \times \pi
5. Express the final answer as a multiple of \pi: \frac{\pi}{4}

Key Concepts

Degree to Radian Conversion

To convert degrees to radians, use the conversion factor π radians = 180 degrees. This means that to convert a degree measure, you multiply the degree value by π/180. For example, to convert 45°, you would calculate 45 × (π/180), simplifying to π/4 radians.

Understanding Radians

Radians are a unit of angular measure used in mathematics, particularly in trigonometry. One radian is defined as the angle created when the arc length is equal to the radius of the circle. This unit is more natural for mathematical calculations involving circles and periodic functions compared to degrees.

Simplifying Fractions

When converting degrees to radians, the resulting fraction often needs simplification. This involves reducing the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). For instance, in the conversion of 45° to radians, π/4 is already in its simplest form.