Question

1. convert the following degrees into their positive radian measures between 0π and 2π.

a. 54° b. 75° c. -180° d. 227° e. -325° f. 207°

Explanation:

Step1: Use the conversion formula

To convert degrees to radians, use the formula \( \text{Radians}=\frac{\pi}{180}\times\text{Degrees} \).

Step2: Calculate for each part

• a. For \(54^{\circ}\)

$$
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• b. For \(75^{\circ}\)

$$
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• c. For \(- 180^{\circ}\)

$$
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Since we need positive radian measures between \(0\pi\) and \(2\pi\), \(-\pi + 2\pi=\pi\)

• d. For \(227^{\circ}\)

$$
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• e. For \(-325^{\circ}\)

$$
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\(-\frac{65\pi}{36}+2\pi=-\frac{65\pi}{36}+\frac{72\pi}{36}=\frac{7\pi}{36}\)

• f. For \(207^{\circ}\)

$$
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$$

Answer:

a. \(\frac{3\pi}{10}\)
b. \(\frac{5\pi}{12}\)
c. \(\pi\)
d. \(\frac{227\pi}{180}\)
e. \(\frac{7\pi}{36}\)
f. \(\frac{23\pi}{20}\)