Textbook Question
Work each problem.
Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?
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1. Measuring Angles
Complementary and Supplementary Angles
Problem 9
Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π.
800°
Verified step by step guidance1
Recall the conversion formula from degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(800^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{800}{180}\) by dividing numerator and denominator by their greatest common divisor.
Express the simplified fraction multiplied by \(\pi\) to write the answer as a multiple of \(\pi\).
If desired, convert the improper fraction to a mixed number to express the radian measure in a clearer form.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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 angles in terms of π allows for exact values rather than decimal approximations, which is useful in trigonometric calculations.
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Simplifying Radicals and Fractions
After converting degrees to radians, the resulting fraction should be simplified by dividing numerator and denominator by their greatest common divisor. This simplification makes the radian measure clearer and easier to interpret, especially when expressed as a multiple of π.
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