Question

convert the angle to decimal degrees and round to the nearest hundredth of a degree. 3) 57°25 27 a) 57.48° b) 57.43° c) 57.38° d) 57.42° find the angle of least positive measure coterminal with the given angle. 4) -116° a) 424° b) 244° c) 64° d) 116°

Explanation:

3.

Step1: Recall the conversion formula

1 degree = 60 minutes. So to convert minutes to degrees, divide by 60. Given $57^{\circ}25'$, we convert 25 minutes to degrees.
Let $x$ be the decimal - degree equivalent of 25 minutes. Then $x=\frac{25}{60}\approx0.42$.

Step2: Add the degree part and the decimal - degree part

The decimal - degree measure of the angle is $57 + 0.42=57.42^{\circ}$.

Step1: Recall the concept of coterminal angles

Coterminal angles differ by a multiple of $360^{\circ}$. Let the given angle be $\theta=- 116^{\circ}$. We want to find a positive coterminal angle.
We add $360^{\circ}$ to $\theta$. Let $\alpha$ be the positive coterminal angle. Then $\alpha=-116^{\circ}+360^{\circ}$.

Step2: Calculate the positive coterminal angle

$\alpha = 244^{\circ}$.

Answer:

D. $57.42^{\circ}$

4.