Problem 3 70 .pdf
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Title: Microsoft Word - 3.2.3 3-70
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3-70. DERIVATIVES OF SINE AND COSINE GRAPHICALLY
It appears that the derivatives of sine and cosine are related. What about the second
You will be given a resource page with five sets of axes, vertically aligned. The x-axis is scaled
from [−2ߨ, 2ߨ] by ଶ , and the y-axis is scaled from [−2, 2] by 1.
a. Sketch as accurately as you can ݂ሺݔሻ = sin ݔon the top set of axes. Draw bold dots on
all maximum and minimum points.
b. On the second set of axes, sketch ݂ ′ሺݔሻ (found in 3-69) as accurately as you can.
c. Compare the graph of ݂ሺݔሻ with ݂ ′ሺݔሻ. What does ݂ሺݔሻ look like when ݂ ′ሺݔሻ = 0?
Your teacher will show you how to use Desmos to find the slopes of tangent lines along
the curve. These slopes of ݂ሺݔሻ can be plotted to result in the same ݂ ′ሺݔሻ graph that
you created on your resource page. For this demonstration, visit:
d. Repeat the Desmos process for ݂″ሺݔሻ, ݂′″ሺݔሻ, and ݂ ௩ ሺݔሻ, the second, third and fourth
derivatives of ݂ሺݔሻ.
To create ݂″ሺݔሻ, visit: http://tinyurl.com/FXtrig2
To create ݂′″ሺݔሻ, visit: http://tinyurl.com/FXtrig3
To create ݂ ௩ ሺݔሻ, visit: http://tinyurl.com/FXtrig4
e. What do you notice about ݂ ௩ ሺݔሻ ?
f. Predict ݂ ଶ ሺݔሻ and ݂ ଵଵ ሺݔሻ.
݂ ௩ ሺݔሻ
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