The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Courses » ap-calculus

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: [ap-calculus] appearance of radians in calculus problems
Replies: 1   Last Post: Oct 22, 2012 5:39 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Riddle, Ginger

Posts: 10
Registered: 7/13/08
[ap-calculus] appearance of radians in calculus problems
Posted: Oct 22, 2012 4:38 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

This ap-calculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus
Teacher Community Forum at
and post messages there.
It has been very interesting to read what teachers say about this topic!

I tell my students that angle measure changes are in radians because the trig derivatives and integrals we memorize only work in radians.

Consider two graphs of the sine, one with the x-axis expressed in degrees, and the other in radians. Look at an average rate of change over, for example, pi/6 to pi/4 on the radian graph, or 30 to 45 degrees. The change in y is the same, but the change in the degree measures are different. The radian graph gives us a rate of change of (sqrt(2)-1)/2 divided by pi/12, but the degree graph gives us (sqrt(2)-1)/2 divided by 15-not the same number at all!

Therefore, as we look at the instantaneous rate of change, the derivatives are different if we use degrees instead of radians. The derivative of the sine is the cosine if angles are expressed in radians, but if the angles are in degrees, the derivative of the sine is the cosine times (180/pi). Yuk. And the second derivative of the sine is negative sine times (180/pi)^2.

When I introduce the derivative of the sine function, I have the kids graph the derivative function on their calculators. Y1=sin(x), Y2=nDeriv(Y1,X,X). In the past I have made sure they are in radian mode before we start. Now, maybe I'll change that! If we try this in degree mode (even if we change the window to x = -360 to 360), the derivative doesn't resemble the value of the slope until we convert to degrees. (It IS the value of the slope, just in degree mode.)

I don't know how well I've explained this, but it seems to make sense to my students.

Ginger Riddle
Leavenworth, Ks

To search the list archives for previous posts go to

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.