Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 450°

Verified step by step guidance

1. Convert the degree measure to radians using the formula: radians = degrees \times \frac{\pi}{180}
2. Substitute 450° into the formula: radians = 450 \times \frac{\pi}{180}
3. Simplify the fraction \frac{450}{180} to its simplest form.
4. Express the simplified fraction as a multiple of \pi.
5. Write the final answer as a multiple of \pi.

Key Concepts

Degree and Radian Measures

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 450°, you would calculate 450 × (π/180), simplifying the expression to express the angle in terms of π.

Simplifying Radian Measures

After converting degrees to radians, it is often necessary to simplify the resulting expression. This involves reducing the fraction to its simplest form, which may include factoring out common terms. For instance, in the case of 450°, the conversion yields 5π/2, which is already in its simplest form, illustrating the importance of simplification in trigonometric calculations.