Question

1. quelle est la mesure, en degré décimal, des angles suivants ?

a) 4,28 rad
b) 0,25 rad
c) -80°305

Explanation:

Step1: Recall conversion formula

We know that to convert radians to degrees, we use the formula $\text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}$.

Step2: Convert 0.25 rad to degrees

$0.25\times\frac{180^{\circ}}{\pi}=\frac{45^{\circ}}{\pi}\approx 14.32^{\circ}$

Step3: Convert 4.28 rad to degrees

$4.28\times\frac{180^{\circ}}{\pi}=\frac{770.4^{\circ}}{\pi}\approx 245.23^{\circ}$

Step4: Convert - 80°30'5'' to decimal - degrees

1. First, convert minutes and seconds to degrees.

• 1 degree = 60 minutes, so 30 minutes $=\frac{30}{60}=0.5^{\circ}$.
• 1 degree = 3600 seconds, so 5 seconds $=\frac{5}{3600}\approx0.0014^{\circ}$.

1. Then, add them to the degree part.

• $-80^{\circ}30'5''=- (80 + 0.5+0.0014)^{\circ}=-80.5014^{\circ}$

Answer:

a) Approximately $245.23^{\circ}$
b) Approximately $14.32^{\circ}$
c) Approximately $- 80.5014^{\circ}$