Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ 150°

Verified step by step guidance

1. Understand that to convert degrees to radians, you use the conversion factor \( \frac{\pi}{180} \).
2. Multiply the degree measure by the conversion factor: \( 150° \times \frac{\pi}{180} \).
3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
4. Recognize that \( 150 \div 30 = 5 \) and \( 180 \div 30 = 6 \), so the fraction simplifies to \( \frac{5\pi}{6} \).
5. Conclude that the degree measure of 150° is equivalent to \( \frac{5\pi}{6} \) radians.

Key Concepts

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. To convert degrees to radians, the formula used is: radians = degrees × (π/180). Understanding this relationship is essential for converting angle measures accurately.

Conversion Formula

The conversion formula from degrees to radians is crucial for solving problems involving angle measures. Specifically, to convert an angle in degrees to radians, multiply the degree measure by π and then divide by 180. For example, to convert 150°, you would calculate 150 × (π/180), simplifying to 5π/6 radians.

Simplifying Fractions

Simplifying fractions is an important skill in mathematics, particularly when converting degrees to radians. After applying the conversion formula, it is often necessary to reduce the resulting fraction to its simplest form. This ensures clarity and precision in mathematical communication, especially when expressing answers as multiples of π.