Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 90°

Verified step by step guidance

Understand that to convert degrees to radians, you use the conversion factor \( \frac{\pi}{180} \).

Multiply the degree measure by \( \frac{\pi}{180} \).

For 90°, set up the multiplication: \( 90° \times \frac{\pi}{180} \).

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.

Express the result as a multiple of \( \pi \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Degree and Radian Measure

Degrees and radians are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. Understanding the relationship between these two units is essential for converting angles from one measure to another.

Conversion Formula

To convert degrees to radians, the formula used is: radians = degrees × (π/180). This formula allows for the straightforward conversion of any angle measured in degrees into its corresponding radian measure.

Multiples of π

When expressing angles in radians, it is common to leave the answer as a multiple of π. For example, 90° converts to π/2 radians, which is expressed as a multiple of π. This notation is useful for simplifying calculations and understanding the relationship between angles.

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