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


45°

Verified step by step guidance

1. Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
2. Substitute the given degree measure into the formula: \(45^\circ \times \frac{\pi}{180}\).
3. Simplify the fraction \(\frac{45}{180}\) by dividing numerator and denominator by their greatest common divisor.
4. Express the simplified fraction multiplied by \(\pi\) to write the answer as a multiple of \(\pi\).
5. Write the final answer in the form \(\frac{\text{numerator}}{\text{denominator}}\pi\) without calculating the decimal value.

Key Concepts

Degree to Radian Conversion

Degrees and radians are two units for measuring angles. To convert degrees to radians, multiply the degree measure by π/180. This conversion is essential because radians are the standard unit in many mathematical contexts, especially calculus and trigonometry.

Understanding π as a Constant

π (pi) is an irrational constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter. Expressing answers as multiples of π keeps the result exact and avoids decimal approximations, which is preferred in trigonometry.

Simplifying Fractions in Radian Measures

After converting degrees to radians, the resulting fraction involving π should be simplified if possible. Simplifying fractions makes the radian measure clearer and easier to use in further calculations or interpretations.