You will need the following items: scissors, plate, 5 different colored pencils, protractor, paper to answer questions

Transcription

1 Radian measure task You will need the following items: scissors, plate, 5 different colored pencils, protractor, paper to answer questions Instructions will follow on each slide. Feb 19 10:33 AM Step 1 Take your paper plate, and fold it into fourths. The plate may be too thick to do two folds at once, so the best method is to fold it in half, then unfold, then fold for the other direction. You need to create two perpendicular diameters on the plate. Feb 19 10:34 AM 1

2 Step 2 Using one of the colored pencils, draw one radius from the center out to the right of the plate along the fold line. We will label this 0. Place the label for 0 towards the edge of the plate. Step 3 We need to form a right angle, from the first radius. This angle needs to have a radius that is drawn up from the first radius. Use a second colored pencil to form this radius. Label the top of the plate as 90 degrees. Feb 19 10:36 AM Step 4 Finish out the remaining lines with the two additional colors. Label each with its correct angle measurement, ending back at 0. When you reach 0, you need to also re label this angle as 360. Feb 19 10:39 AM 2

3 Step 5 Retrieve a piece of string from your teacher. Cut the string to fit the length of the radius of your plate. (Remember, the radius is half of the diameter of the circle.) We will use this length of string and the last remaining colored pencil for measurements. Feb 19 10:40 AM Step 6 Starting at 0 on the outside of the plate, use your string radius to mark the length around the outside of the circle. Place a mark at the end of the length and label this as 1. Re locate the string to 1, and measure from that point to the end of the radius string. Label this ending mark as 2. Repeat this process, labeling each ending mark. Until you reach the starting point of 0. DO NOT GO PAST 0. Feb 19 10:41 AM 3

4 Questions to answer: How many marks did you make? Did you end up at exactly zero? Approximately, how much more of your radius is needed to reach zero? Feb 19 10:46 AM Measure the length of your radius, and times it by 6.2 (It should take approximately 6.2 radii around your circle). What does this number represent in relationship to the length of the circle? Feb 19 10:48 AM 4

5 What is the formula for the circumference of a circle? Use this formula and your radius length to calculate the circumference. Feb 19 10:48 AM Step 7 Using a protractor, measure the angle from 0 to the first mark. How big is this angle? Measure to the second mark. How big is this angle? Measure all angles through mark 6. Feb 19 10:50 AM 5

6 The first angle is 57 degrees and every mark after is an increase of 57 degrees. One radian is the measure of the central angle of the circle. Feb 19 10:51 AM There is a relationship between radians and the degrees of a circle. For an entire circle, radians = degrees For half of a circle, radians = degrees Feb 19 10:52 AM 6

7 90 o = radians 270 o = radians 30 o = radians What type of a formula can we generate to convert radians to degrees or degrees to radians? Feb 19 10:53 AM Degrees to radians: number of degrees * **reduce radians to degrees: radians * Feb 19 10:54 AM 7

8 Step 8 Use the protractor to fill in missing angles. Let's put angles at 30 degrees, 45 degrees, and 60 degrees. Label on the plate and convert these to radians. Feb 19 10:56 AM Use your paper to make the following conversions: convert from radians to degrees Feb 19 10:57 AM 8

9 Convert from degrees to radians (do not use decimals and leave the pi in the final answer) 315 o = 190 o = 98 o = 222 o = 60 o = 931 o = Feb 19 3:34 PM What does a negative angle tell you? What does an angle that exceeds 360 degrees or 2 pi tell you? Feb 19 3:35 PM 9

10 Draw each angle. If the angle exceeds 360 or 2 pi, then you will have a full revolution plus the additional movement Feb 19 3:45 PM Feb 19 3:48 PM 10

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