Transformations of
Trigonometric Functions
Sine and Cosine
Startup
Accessing Background Knowledge
 Work with your partner to answer the question
written on the board; AT LEAST 3 POINTS
 Find someone wearing the same color shirt as you.
Trade ideas, and add to your list. ADD AT LEAST 2
POINTS that you didn’t already have.
 Form into groups of 4. Add to your lists, and be ready
to share 1 thing with the class that you remember.
Gather Your Supplies
 1 yardstick
 1 wax paper strip
 1 poster marker
 1 Sharpie marker
 2 pieces of tape
 Your paper plate and ½ sheet of graphs
(optional)
 Return to your seats
Round 1: Graph the parent function
(Text to graph)
 On the poster, graph a well-labeled, accurate set of
axes for graphing trig functions
 Graph your assigned parent function, written on the
poster paper
 Make the distance from 0 to 1 on the y-axis to be about
5 inches.
 Mark at least 5 “important” points on the graph (i.e.
maxima, minima, zeros, etc.)
 Using tape, hang the strip of wax paper over your
function; trace the parent function onto the wax
paper, including the 5 important points
 Return to your seats
Round 2: Inference about “h”
(Text to graph)
 Background knowledge: Tell your partner what you
remember about the role of “h” in the equation
y
= a(x-h)2 + k
 Make an inference about what “h” will do in a trig function
 Move 1 poster to the right. Check the work of the previous
pair, and discuss any questions with them
 Take card “h” off the wall. Look at the transformation of
the parent function, and move the wax paper as indicated
by “h”. Hang the wax paper in its new spot, and hang “h”
back on the wall face-up.
 Return to your seats
Round 3: Inference about “k”
(Text to graph)
 Background knowledge: Tell your partner what you
remember about the role of “k” in the equation
y = a(x-h)2 + k
 Make an inference about what “k” will do in a trig function
 Move 1 poster to the right. Check the work of the previous
pair, and discuss any questions with them.
 Take card “k” off the wall. Look at the transformation of
the parent function, and move the wax paper as indicated
by “k”. Hang the wax paper in its new spot, and hang “k”
back on the wall face-up.
 Return to your seats
Round 4: Inference about “a”
(Text to graph)
 Background knowledge: Tell your partner what you
remember about the role of “a” in the equation
y = a(x-h)2 + k
 Make an inference about what “a” will do in a trig function
 Move 1 poster to the right. Check the work of the previous
pair, and discuss any questions with them.
 Take card “a” off the wall. Look at the transformation of
the parent function. This time, draw your transformed
function directly onto the poster using a DIFFERENT
COLOR than the parent function.
 Throw away your wax paper. Place cards “h”, “k”, and “a”
into the correct bins on the desk.
 Return to your seats
Round 5: Graph to Text
 Rotate 1 poster to the right. Check the work; discuss
any questions with the previous pair.
 Using the equation of the parent function with the
graph of the transformed function, write the
equation of the transformed function onto the poster
paper.
 Return all materials.
 Return to your seats.
With Your Partner........
 Sketch the graph of the function
f(x) = 2 sin (θ - π) - 1
With your partner…..
 Where on the x-axis would the zeros be for the
equation…
 f(x) = cos (θ - π) + 1
 f(x) = tan (θ + π) – 1
 f(x) = sin (θ – π/2)
Exit Slip
 Hand in your exit slip as you leave class.
 NO NEW HOMEWORK tonight…make sure you’ve
finished all previous homework.
 Mrs. Lee will teach class tomorrow. I expect to
receive another EXCELLENT report! 