# Radians and Degrees Worksheets

This are both units of measure that are used to express the distance between two lines that meet at a point and form an angle. We often begin to use units of degrees early in our academic career because they are a little easier to understand. We begin by using a protractor to determine the number of degrees between each of the lines that form an angle. As we move on to learning calculus and advanced trigonometry radians become used much more because they are easier to use when manipulating and evaluating complicated expressions and equations. These worksheets and lessons help students learn to calculate radians and degree values as well as measuring the length of arc of a circle.

### Aligned Standard: HSF-TF.A.1

- Right Angle to Radians Step-by-step Lesson - A simple conversion to get you to kick it off.
- Guided Lesson - Radians to degrees, calculate the length of an arc, the area of a face-off circle.
- Guided Lesson Explanation - These are very intimidating questions, but they are not that hard to tackle.
- Practice Worksheet - I set this diverse set of questions up to challenge thought cycles.
- Matching Worksheet - This can be a skimmer activities because I included all the units.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Each sheet is dedicated to one of the problem types.

- Homework 1 - To go from degrees to radians: take the value of degrees and multiply it by Pi divided by one-hundred and eighty degrees.
- Homework 2 - s = Θ r
- Homework 3 - A section of faceoff circle in a hockey rink is a circular sector with a radius of 3.92 m and a central angle of 60.5°. What is the area of this section of the faceoff circle?

### Practice Worksheets

Ice hockey faceoff circle geometry; why not!

- Practice 1 - How long is the arc subtended by an angle of 9Π/14 radians on a circle of radius 12 cm?
- Practice 2 - A section of faceoff circle in a hockey rink is a circular sector with a radius of 6.45 m and a central angle of 78.6°. What is the area of this section of the faceoff circle?
- Practice 3 - A section of side walk has a circular sector. The radius is 2.30m and a central angle 90°. What is the area of this section of sidewalk?

### Math Skill Quizzes

You thought you escaped the faceoffs? Not quite yet!

- Quiz 1 - Convert Π/16 to degrees.
- Quiz 2 - Convert 80° to radians.
- Quiz 3 - Barry the Beaver gnaws his way through a circular section wood. The sector has a radius of 6.90 m and central angle 95.3°. What is the area of this section of wood?

### Getting to Know Radians and Degrees

When we learn the concepts of geometry, the first thing we come across is measuring an angle. This is the first step towards completely understanding the concept of geometry. When two lines meet each other at a specific point, the distance between those lines is called an angle. Radian and degrees are the two different units that can be used to measure an angle.

We often begin using the degree unit to measure the size of an angle, this unit also express a sense of direction. This is unit is often easier to understand, and we even see this unit make its way into pop culture in American. Degrees are based on the geometry of a circle that has 360 degrees all the way around it. Originally when mathematicians were trying to decide on which if these units to popularize, degree stood out because it was pretty close to the number of days that were in a calendar year and people were pretty familiar with that.

You will find radians start to peak its head later in high school and trigonometry and calculus classes. This unit is often used when you are working with smaller numbers. One radian is the angle formed when an arc opposite to the angle is the same as the radius of the circle. Therefore, a radian is truly a ratio between the displaced arc length and the radius. A radian is the equivalent of 180 degrees due to the fact that 2 radians is equal to a circle (360 degrees).

### What is Arc Length?

When you look at a circle and choose a piece of the circumference, you have chosen an arc. The distance of this curve is called arc length. There are two math formulas for determining this length, based on the types of units you are using to measure the bend in the curve.

For radians we use the formula: Arc length = Θ x r

For degrees we use the formula: Arc length = (Θ x π/180) r