Download TPC Sec 2.3

EQ: Which of the trigonometric functions
are positive and which are negative in each
of the four quadrants?
SECTION 2.3
Warm-Up/Activator
Name the quadrants of the Coordinate
(Cartesian) Plane – use drawing on next slide.
 Label the signs of x and y in each quadrant
 Which coordinate is sin and which
coordinate is cos  ?
 Label the signs of the sine and cosine in
each quadrant.

Drawing for the Warm-up/Activator
How does tangent relate to sine and cosine?
O
tan  
A
So, by multiplying the top and bottom of the fraction by 1/H it follows that
O
tan   
A
1
O
H  H  sin 
1
A cos 
H
H
sin 
tan  
cos 
-+
S
T
--
ALL STUDENTS TAKE CALCULUS
++
P(cosΘ, sinΘ)
(x , y)
sin   
sin   
cos   
cos   
tan   
tan   
sin   
sin   
cos   
cos   
tan   
tan   
A
C
+-
Reference Right Triangle
Drop a perpendicular from the terminal side to the x-axis and then
you have a right triangle with the reference angle as one of the acute
angles.
Starter Examples:
Find the reference angle for each of the
following, then determine the value of the
function based on special or quadranal
angles, and the location of the terminal
side.
1) sin 300
3) tan 225
2) cos 150
45
30
ref < 60
+
Sign
tan
45
cos
30
- sin 60

3

2
3

2
1
Example 4
Find the reference angle for each angle
given.
 (a) 210˚


(b) 135˚

(c) 422˚
Your Turn 4
Find the reference angle for each angle
given.
 (a) 160˚


(b) 285˚

(c) 600˚
Example 5 & Your Turn 5

Find the exact value of cos 210˚

Find the exact value of sin 330˚
Example 6 & Your Turn 6

Find the exact value of tan 495˚

Find the exact value of tan 660˚
Example 7 & Your Turn 7

Find the exact value of csc (-210˚)

Find the exact value of sec (-330˚)
Example 8 & Your Turn 8

Find all values of  where 0    360
3
sin



when
2

Find all values of  where 0    360
3
when cos    2
Example 9 & Your Turn 9

Use a calculator to approximate the following

a) tan 466˚

Use a calculator to approximate the following

a) sec (-118˚)
b) csc (-313˚)
b) cot (226˚)
Example 10 & Your Turn 10
Example 11 & Your Turn 11
