Download Notes 1.3 Day 2.jnt

College Math Survey
Notes 1.3 Part 2
Mathematician:
Thursday 8/28/14
Part 1 – Signs of the 6 Trig Functions
Let (x, y) be a point other the origin on the terminal side of an angle  in standard
position. The distance from the point to the origin is
r  x 2  y 2 . The six
trigonometric functions of  are defined as follows.
P (x, y)
csc  
cos  
sec  
tan  
cot  
y
x
Ex 1:
sin  
All Students Take Calculus
Suppose that (x, y) is in the indicated quadrant. Decide whether the given ratio is positive or
negative.
A)
III,
r
x
B)
II,
x
y
C)
IV,
x
r
Part 2 - Quadrantal Angles
______________________________________________________________________
Ex 2:
Find the values of the six trig functions of a
sin  
csc  
cos  
sec  
tan  
cot  
90 angle.
Ex 3:
Find the values of the six trig functions of a
sin  
csc  
cos  
sec  
tan  
cot  
180 angle.
Undefined Function Values
If the terminal side of a quadrantal angle lies along the y-axis, then
.
If the terminal side of a quadrantal angle lies along the x-axis, then
.
Ex 4:

Find the values of the six trig functions of
sin 
0,90,180, 270, 360
cos  tan  cot 
sec 
csc
0
90
180
270
360
Ex 5:
Use the trig function values of quadrantal angles to evaluate each expression.
a)
tan 0  6sin 90
b)
2 sec 0  4 cot 2 90  cos 360
College Math Survey
Homework 1.3 Part 2
Mathematician:
Suppose that the point (x, y) is in the indicated quadrant. Decide whether the given ratio is
positive or negative. Hint: Drawing a sketch may help.
17)
II,
x
r
18)
III,
y
r
19)
IV,
y
x
20)
IV,
x
y
x2 = x  x
Note:
cos2 90o = cos90o cos90o
33)
cos 90O + 3 sin 270 O
34)
tan 0 O – 6 sin 90 O
35)
3 sec 180 O – 5 tan 360 O
36)
4 csc 270 O + 3 cos 180 O
37)
tan 360 O + 4 sin 180 O
38)
2 sec 0 O + 4 cot2 90 O + cos 360 O
Find the values of the six trigonometric functions for each angle in standard position having the
given point on its terminal side.
41)
(-4, -3)
42)
(-5, 12)
sin  
csc  
sin  
csc  
cos  
sec  
cos  
sec  
tan  
cot  
tan  
cot  