Activity 5.3.1 Radians and Degrees You are used to measuring angles in degrees. Another unit of angle measure is called a radian. This activity explores the relationship between degrees and radians. Open the file ctcoregeomACT531.gbb. Observe the five angles shown: From the View menu, select Algebra to reveal the Algebra Panel on the left side of the screen. Double click on the angle in the algebra window to select Object Properties. Look above the panel for the Properties of You will see five buttons. Choose the Angle α. rightmost button that looks like the one at the farthest right side. Click on Radians to convert from degrees to radians. Notice that the 45° angle measures approximately 0.79 radians, and that radians. Record the other radian measures in 180° = π the table below, both in terms of and as decimal approximations. π Angles Measure in Degrees Radians (decimal Radians (in terms of π) approximation) 45° 0.79 90° 180° π 270° 360° Examine the results of your table and work with a partner to come up with an equation that relates degree measure to radian measure. Use your equation to convert the following angle measures to radian measures: a. 30° b. 60° c. 120° d. 75° A simple definition for a radian is: the measure of an angle at the center of a circle that intercepts an arc whose length is equal to the radius of the circle. To visualize scroll down in the Geogebra file to find points and Use the Angle with K L. Given Size Tool in Geogebra to create a 1 radian angle with vertex and side K , by typing “1
Activity 5.3.1 Radians and Degrees You are used to measuring angles in degrees. Another unit of angle measure is called a radian. This activity explores the relationship between degrees and radians. Open the file ctcoregeomACT531.gbb. Observe the five angles shown: From the View menu, select Algebra to reveal the Algebra Panel on the left side of the screen. Double click on the angle in the algebra window to select Object Properties. Look above the panel for the Properties of Angle α. You will see five buttons. Choose the rightmost button that looks like the one at the farthest right side. Click on Radians to convert from degrees to radians. Notice that the 45° angle measures approximately 0.79 radians, and that 180° = π radians. Record the other radian measures in the table below, both in terms of π and as decimal approximations. Angles Measure in Degrees Radians (decimal approximation) Radians (in terms of π) 45° 0.79 90° 180° π 270° 360° Examine the results of your table and work with a partner to come up with an equation that relates degree measure to radian measure. Use your equation to convert the following angle measures to radian measures: a. 30° b. 60° c. 120° d. 75° A simple definition for a radian is: the measure of an angle at the center of a circle that intercepts an arc whose length is equal to the radius of the circle. To visualize scroll down in the Geogebra file to find points K and L. Use the Angle with Given Size Tool in Geogebra to create a 1 radian angle with vertex K and side , by typing “1
Activity_5_3_1.docx