College Trigonometry, 2011a

962 Applications of Trigonometry
(b) For f(θ) =5sin(2θ), show that f ( π − π 4
)
≠ f
( π
4
)
,yetthegraphofr =5sin(2θ) is
symmetric about the y-axis. (See Example 11.5.2 number 3.)
In Section 1.7, we discussed transformations of graphs.
classmates explore transformations of polar graphs.
In Exercise 65 we have you and your
65. For Exercises 65a and 65b below, let f(θ) = cos(θ) andg(θ) =2− sin(θ).
(a) Using your graphing calculator, compare the graph of r = f(θ) to each of the graphs of
r = f ( θ + π ) ( ) ( ) ( )
4 , r = f θ +
3π
4 , r = f θ −
π
4 and r = f θ −
3π
4 . Repeat this process
for g(θ). In general, how do you think the graph of r = f(θ + α) compares with the
graph of r = f(θ)?
(b) Using your graphing calculator, compare the graph of r = f(θ) to each of the graphs of
r =2f (θ), r = 1 2f (θ), r = −f (θ) andr = −3f(θ). Repeat this process for g(θ). In
general, how do you think the graph of r = k ·f(θ) compares with the graph of r = f(θ)?
(Does it matter if k>0ork