Math 1016: Elementary Calculus with Trigonometry I
Ch. 4 Techniques of Differentiation with Applications
Tangent Lines to Graphs of Trigonometric Functions
I.
Steps
1. Graph the curve of the trig function
2. Find tangent line to curve at specific point(s)
3. Sketch tangent line(s) to the curve of the trig function
II.
Examples
1. Graph the curve of
x
sin(x)
2sin(x)
y = 2sin(x) −1 along with the tangent lines through x =
2sin(x) − 1
(x,y)
3
2
1
-1
-2
-3
π
π
and x = .
6
2
2. Graph the curve of
x
2x
cos(2x)
y = 3cos(2x) along with the tangent lines through x =
3cos(2x)
(x,y)
3
2
1
-1
-2
-3
π
4
and
x=
π
2
.
3. Find the equation of the tangent line to the curve
4. Determine the point(s) where
y = 3 + 12 x + sin x at the point (0,3).
y = cos x + 3 sin x has horizontal tangent(s).