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4.3b-Trigonometric Functions on the
Unit Circle
Task
What is the main activity that students
will be working on in this lesson?
Students will begin class with their second
mad minute on degrees. They will complete a
warm-up on the first half of lesson 4.3.
Students will learn how to use reference angles
to compute one of the six trig functions. They
will practice finding reference angles and then
using a table on page 245 will find the answer
to the function they are trying to solve. Then
they will learn how to find the five remaining
trig functions given a function and a
restriction. Students will use their CAST chart
to locate the quadrant that their angle is in and
then solve for r and the other functions. Last,
students will complete their unit circle by
adding in all the coordinate points for each
angle. They will then use the points to find a
trig function at a particular angle when the
radius is one.
Assignment: pg.251 #25-59 odd
Instructional Support
What tools or resources will students have to use in their
work that will give them entry to, and help them reason
through, the activity?
Students may use the chart on pg. 245 that has the values for sin,
cos, and tan for angles 30,45, and 60.
Students may refer to their CAST chart in their notes and book,
pg.245, in order to figure out the appropriate sign of function given
a specific angle.
Students may use their circles once they have recorded all the
coordinate points to complete the last section of hw. They may also
use the unit circle on pg.248 that has everything filled in. LAST, they
may resort to using their calculators to solve the functions.
What questions might you ask students that will support
their exploration of the activity and bridge between what
they did and what you want them to learn (the two
green boxes)?
They will be able to calculate trig functions for
any given angle using reference angles.
They will be able to find all six trig functions
given one trig function and a restriction.
They will be able to compute the exact value of
a trig function given any angle in the unit circle.
Students will learn what the unit circle is and
how to use the coordinate points provided on
the unit circle.
To be clear on what students actually did, begin by asking a set of
assessing questions such as: What did you do? How did you get
that? What does this mean? Once you have a clearer sense of what
the student understands, move on to appropriate set of questions
below.
What are the various ways that students How do we calculate reference angles given any particular angle?
What do you subtract an angle from usually?
might complete the activity?
#25-32: find the reference angle, match the
function and angle with the grid on pg.245, and
then use the CAST chart to find the quad and
sign of the function. OR use their calculator to
solve.
#33-40: find the sign of given statements,
match the signs with the appropriate quadrant
in CAST, draw the triangle, find r, and solve six
trig functions.
#43-59: Use the unit circle to compute the trig
functions with the given coordinate points. OR
put in calculator OR use triangles to solve.
Learning Goals (Residue)
What understandings will students take
away from this activity?
What is the sign of something if it is less than zero?
What can you refer to in order to figure out the sign of a trig
function?
What does CAST stand for? How can you use the mnemonic device
CAST to solve for trig functions?
What do you use find r? What is the trick we use for our inverse
functions csc, sec, and cot?
What does the unit circle mean? What is r equal to? How do we use
the unit circle to solve for trig functions?
What does the coordinate point P(x,y) stand for in the unit circle?
How do we know that sine is the y coordinate and cosine is x
coordinate? What can we refer to in order to prove this?
Evidence
What will students say, do, produce, etc.
that will provide evidence of their
understandings?
Students will complete their second mad minute
on degrees, mad minute on radians and then
will complete the assignment on pg.251.
Students will have a quiz on sections 4.1-4.3
next.
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