Radians

Polar_Gradian_Scale

Starter activity: When the metric system was introduced after the French revolution, at first things were also changed so that there were now 100 “gradians” in a right angle, not 90 degrees, and 10 days a week, not 7. The main bits of the metric system have spread from France to almost the whole world, French artillery still uses gradians, and you have gradians as an option on your calculator – but those new measures of angles and of time were soon mostly dropped even in France. Why were they dropped?

 

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graph4_radian_polar

Activity

Learn about how to do degrees and radians on your calculator.

The calculator is told to take degrees or radians as its unit for angles in Setup (Shift>Mode).

If you have selected degrees as the unit, you can convert radians to degrees by entering the number, pressing DRG (Shift>Ans), and selecting r to indicate that it is radians you are converting.

calc-radians

If you have selected radians as the unit, you can convert degrees to radians by entering the number, pressing DRG (Shift>Ans), and selecting o to indicate that it is degrees you are converting.

Use your calculator to convert these to radians: 360 degrees, 30 degrees, 180 degrees, 60 degrees, 90 degrees, 45 degrees

Convert these to degrees: π/6, 2π, π/4, π, π/3, π/2

SINE AND COS OF ANGLES BIGGER THAN 90 (π/2)

Set your calculator to degrees and find:

sine (91), sine (180), sine (270), sine (360)

What do these mean?

Look here to see what they mean

Activity

Set your calculator to radians. For the following angles, guess sine of the angle from the graph on the whiteboard, and then check your guess with the calculator.

π/6, 2π, π/4, π, π/2, 3π/2

One of the reasons why mathematicians usually use radians is that if we measure in radians,

d/dx(sin x) = cos x, and d/dx(cos x)=−sin x