Question

convert the given angle to decimal degrees.

1. 357°3456\

convert the radian measure to degree measure.

1. 3.2798

a) 187.92°
b) 187.22°
c) 188.42°
d) 188.92°

Explanation:

Step1: Convert seconds to minutes

Since \(1' = 60''\), then \(56''=\frac{56}{60}'\approx0.933'\).

Step2: Add to existing minutes

\(34'+ 0.933'=34.933'\).

Step3: Convert minutes to degrees

Since \(1^{\circ}=60'\), then \(34.933'=\frac{34.933}{60}^{\circ}\approx0.582^{\circ}\).

Step4: Add to existing degrees

\(35^{\circ}+0.582^{\circ}=35.582^{\circ}\).

Step1: Use the conversion formula

The formula to convert radians to degrees is \(x\) radians \(=x\times\frac{180^{\circ}}{\pi}\).

Step2: Substitute the value

For \(x = 3.2798\), we have \(3.2798\times\frac{180^{\circ}}{\pi}\).
Since \(\pi\approx3.1416\), then \(3.2798\times\frac{180}{3.1416}\approx188.42^{\circ}\).

Answer:

\(35.582^{\circ}\)

For problem 13: