March 02, 2014
A) FIND (Do not use your chart.)
cos 150º sin π/4 tan 330º
B)Give the six trig functions for the point
(5,-6).
sin ø =
cos ø =
tan ø =
csc ø =
sec ø =
cot ø =
March 02, 2014
PRECALCULUS
SEC 5.3 PROPERTIES OF THE TRIG
FUNCTIONS
GOALS:
*DETERMINE THE DOMAIN & RANGE
*DETERMINE THE PERIOD OF THE TRIG
FUNCTION
*DETERMINE THE SIGN OF THE TRIG
FUNCTION
*USE PROPERTIES OF TRIG FUNCTIONS
March 02, 2014
APPLICATIONS OF SINE WAVES
Many compression algorithms, like JPEG use fourier transforms that rely on sin and cos.
Surveying, navigation and astronomy all rely on sin and cos for the position of objects and other calculations.
Music is composed of waves of different frequencies and amplitudes and these can be described using sin/cos. In fact
most anything involving sound waves will rely on sin/cos.
Ballistic trajectories rely on sin/cos, and there are numerous other uses of them in physics.
Space flight relies on calculations and conversions to polar coordinates. So do satellites.
GPS and cellphones rely on triangulation and formulas involving sin/cos.
Signal transmission, e.g. TV and radio broadcasting, involves waves described with sin/cos waves.
March 02, 2014
DOMAIN
R
SINE
COSINE
R
TANGENT
ALL R EXCEPT ODD
MULTIPLES OF ∏/2
COSECANT
SECANT
All R except integer
MULTIPLES OF ∏
ALL R EXCEPT ODD
COTANGENT
MULTIPLES OF ∏/2
All R except integer
MULTIPLES OF ∏
RANGE
-1≤y≤1
-1≤y≤1
R
y ≤-1 or y ≥ 1
y ≤ -1 or y ≥ 1
R
March 02, 2014
March 02, 2014
SIN -60º = -SIN 60º = -√3/2
COS -120º = COS 120º = -1/2
March 02, 2014
FIND Tan(π/3 + π) = Tan π/3 = √3
Find cos(45º+360º) = cos 45º = √2/2
March 02, 2014
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March 02, 2014
March 02, 2014
TRIG IDENTITIES
March 02, 2014
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March 02, 2014
sin 73º = .96 what is cos 17º = .96
March 02, 2014
Name the quadrant in which angle ø lies
sin < 0 and cos > 0
csc > 0 and cos < 0
If sin ø = -4/5 and cos ø = 3/5 what is...
tan ø =
csc ø =
sec ø =
March 02, 2014
I
If cos ø = .3 find the value of
cos ø + cos(ø + 2π) + cos(ø + 4π)
What is ...
sin2 59º + cos2 59º =
cot 40º - cos 40º
sin 40º =
sec (-π/18) • cos (35π/18)
=
March 02, 2014
Assignment
sec 5.3 5-15, 35-40, 60-65, 80-84, 90-94
March 02, 2014