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


800°

Verified step by step guidance

1. Convert the degree measure to radians using the formula: radians = degrees \times \frac{\pi}{180}
2. Substitute 800° into the formula: radians = 800 \times \frac{\pi}{180}
3. Simplify the fraction \frac{800}{180} by finding the greatest common divisor of 800 and 180.
4. Express the simplified fraction as a multiple of \pi.
5. Write the final expression as a multiple of \pi, leaving it in terms of \pi.

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 to radians, you multiply the degree value by π/180. For example, to convert 800°, you would calculate 800 × (π/180).

Simplifying Fractions

After converting degrees to radians, it is often necessary to simplify the resulting fraction. This involves reducing the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, in the case of 800/180, both numbers can be divided by 20 to simplify the fraction.

Understanding π in Trigonometry

In trigonometry, π (pi) is a fundamental constant representing the ratio of a circle's circumference to its diameter. It is crucial in expressing angles in radians, as many trigonometric functions are defined in terms of radians rather than degrees. Recognizing π as a key component in radian measures helps in understanding the relationships between angles and their corresponding trigonometric values.