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Chapter 4: Problem 39

Convert the angle measure from degrees to radians. Round to three decimal places. $$45^{\circ}$$

Short Answer

Expert verified
The equivalent of 45 degrees in radians is approximately 0.785 radians.

Step by step solution

01

Set Up the Conversion

Write the given degrees as a fraction over one and set it equal to a variable. Here it is \( x = \frac{45}{1} \) degrees.
02

Apply the Conversion Factor

Multiply the given angle measure (in degrees) by the conversion factor, \( \frac{\pi}{180} \). \( x = \frac{45}{1} \cdot \frac{\pi}{180} \)
03

Simplify the Fraction

Simplify the fraction to find x. If the numerator and the denominator can be both divided by a common factor, do it. In this case, both 45 and 180 are divisible by 45, giving: \( x = \frac{1}{4} \pi \) radians.
04

Calculate Decimal Value

Use the value of \( \pi \) (approximately 3.1416) to calculate the decimal value. In this case, \( x \approx \frac{1}{4} \cdot 3.1416 = 0.7854 \) radians.
05

Round to Three Decimal Places

Finally, round the result to three decimal places if necessary as per the exercise requirements. That gives \( x \approx 0.785 \) radians.

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