Download . What is a reference angle?

NAME _____________________________________________________ DATE ____________________
Algebra 2: Lesson 12-6 Reference Angles and Exact Values
Learning Goals:
1) How do we determine the sign of the six trigonometric functions in each of the quadrants?
2) What is a reference angle and how do we find the reference angle in each quadrant?
3) How do we determine the exact value of a trigonometric expression?
Do Now: Complete the following questions to prepare for today’s lesson.
a) Sketch and label in standard position if
b) If
and
.
, in what quadrant does the terminal side of
lie?
What is a reference angle?



Reference angle is the acute angle formed by the terminal side of the angle and the ___________
Angles in the first quadrant are their own reference angles
) do not have a reference angle.
Quadrantal angles (
Ref. angle = ________
Ref. Angle = ________
Ref. Angle = _______
Ref. Angle = _______
Example #1: a) Sketch the angle b) Shade the reference angle c) Find the measure of the reference
angle
1) 127o
2) 353o
3) 215o
4)
Example #2: Given the reference angle and the specified quadrant, determine the value of the original
angle, .
5) reference angle =
; quadrant II
6) reference angle =
; quadrant IV
7) reference angle =
; quadrant III
8) reference angle =
; quadrant I
Determining the Sign of the 6 Trig Functions
Recall from yesterday’s lesson
In Quadrant I
In Quadrant II
𝜃 is always +
𝜃 is always ______
𝜃 is always +
𝜃 is always ______
𝜃 is always −
𝜃 is always ______
𝜃 is always +
𝜃 is always ______
𝜃 is always −
𝜃 is always ______
𝜃 is always +
𝜃 is always ______
In Quadrant IV
In Quadrant III
𝜃 is always −
𝜃 is always ______
𝜃 is always −
𝜃 is always ______
𝜃 is always −
𝜃 is always ______
𝜃 is always +
𝜃 is always ______
𝜃 is always +
𝜃 is always ______
𝜃 is always −
𝜃 is always ______
Example #3
a) If
Short Cut
side of
S
A
T
C
b) If
side of
c) If
side of
and
, in what quadrant does the terminal
and
, in what quadrant does the terminal
and
, in what quadrant does the terminal
lie?
lie?
lie?
Finding the Exact Value
1) Find the exact value of cos 210
2) Find the exact value of
(
o
PROCEDURE
). Identify the measure of the reference angle.
3) Find the exact value of csc 120 in simplest radical form.
Practice
). Identify
4) Find the exact value of (
the measure of the reference angle.
6) Find the exact value of
(
)
5) Find the exact value of cot 120 in simplest
radical form.
7) Find the exact value of
(
)