Question

trigonometry remediation for quiz unit 3 circle trig basics write each decimal degree measure in measure in decimal degree form to the 1. 21.425° 2. 84°1236 write each degree measure in radians 3. 120°

Explanation:

Step1: Convert decimal degrees to degrees, minutes, and seconds for \(21.425^{\circ}\)

• The whole number part is the degree: \(21^{\circ}\)
• Multiply the decimal part by \(60\) to get minutes: \(0.425\times60 = 25.5'\)
• The whole number part of the result is the minutes: \(25'\)
• Multiply the decimal part of the minutes (\(0.5\)) by \(60\) to get seconds: \(0.5\times60=30''\)

So \(21.425^{\circ}=21^{\circ}25'30''\)

Step2: Convert degrees, minutes, seconds to decimal degrees for \(84^{\circ}12'36''\)

• Use the formula \(D = d+\frac{m}{60}+\frac{s}{3600}\) (where \(D\) is decimal degrees, \(d\) is degrees, \(m\) is minutes, \(s\) is seconds)
• Substitute \(d = 84\), \(m = 12\), \(s = 36\)

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Step3: Convert degrees to radians for \(120^{\circ}\)

• Use the conversion formula \(R=\frac{\pi}{180}\times D\) (where \(R\) is radians, \(D\) is degrees)
• Substitute \(D = 120\)

$$ R=\frac{\pi}{180}\times120=\frac{2\pi}{3}\text{ radians} $$

Answer:

1. \(21^{\circ}25'30''\)
2. \(84.21^{\circ}\)
3. \(\frac{2\pi}{3}\text{ radians}\)