Math  /  Geometry

QuestionAnswer the following. Round your answers to the nearest hundredth. (a) Convert 18π19-\frac{18 \pi}{19} radians to degree measure. \square (b) Convert -2.61 radians to degree measure. \square

Studdy Solution

STEP 1

What is this asking? We need to convert two radian measures, one involving π\pi and one without, into degrees. Watch out! Remember that radians and degrees are different ways of measuring the same thing – angles!
Don't mix up the conversion factor.

STEP 2

1. Convert the first radian measure.
2. Convert the second radian measure.

STEP 3

Alright, let's **start** with 18π19-\frac{18\pi}{19} radians.
We want to turn this into degrees.
The **key** here is knowing that 180180 degrees is equal to π\pi radians.
This means 11 radian is equal to 180π\frac{180}{\pi} degrees.

STEP 4

So, to convert 18π19-\frac{18\pi}{19} radians to degrees, we **multiply** it by 180π\frac{180}{\pi}.
This gives us: 18π19180π-\frac{18\pi}{19} \cdot \frac{180}{\pi}

STEP 5

Notice how the π\pi on the top and the π\pi on the bottom divide to one!
This leaves us with: 1819180-\frac{18}{19} \cdot 180

STEP 6

**Calculating** this gives us approximately 170.53-170.53 degrees.
Remember, we're rounding to the nearest hundredth!

STEP 7

Now, let's **tackle** 2.61-2.61 radians.
We use the same **conversion factor**: 180π\frac{180}{\pi} degrees per radian.

STEP 8

**Multiplying** 2.61-2.61 radians by 180π\frac{180}{\pi} gives us: 2.61180π-2.61 \cdot \frac{180}{\pi}

STEP 9

**Crunching** those numbers, we get approximately 149.54-149.54 degrees, rounded to the nearest hundredth.

STEP 10

(a) 18π19-\frac{18\pi}{19} radians is approximately 170.53-170.53 degrees. (b) 2.61-2.61 radians is approximately 149.54-149.54 degrees.

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