5.3 Day 1 Properties of Trigonometric Functions
March 02, 2009
5.3 Properties of the Trigonometric Functions
Objectives:
• Identify the signs of trig functions for each quadrant
• Find the exact values of the Trig Functions of an angle given: one function and the quadrant.
Feb 26 ­ 9:15 PM
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5.3 Day 1 Properties of Trigonometric Functions
March 02, 2009
Periodic Functions
Because our trigonometric functions continue infinitely, but repeat their values they are called periodic functions.
Each revolution yields the same values for sine and cosine and their cofunctions.
Feb 26 ­ 10:05 PM
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5.3 Day 1 Properties of Trigonometric Functions
March 02, 2009
Find the exact value of the following trigonometric functions.
Feb 26 ­ 10:13 PM
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5.3 Day 1 Properties of Trigonometric Functions
March 02, 2009
Signs of your function depend on which quadrant you are in.
cosine is negative
sine is positive
cosine is positive
sine is positive
(­ , +)
(+ , +)
(­ , ­)
(+ , ­)
cosine is positive
sine is negative
cosine is negative
sine is negative
Feb 26 ­ 10:18 PM
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5.3 Day 1 Properties of Trigonometric Functions
March 02, 2009
Name the quadrant in which the angle θ lies.
1.
sin θ > 0, cos θ < 0
2.
sin θ < 0, tan θ < 0
3.
cos θ > 0, tan θ < 0
Feb 26­11:34 AM
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5.3 Day 1 Properties of Trigonometric Functions
March 02, 2009
Finding the exact values of a trigonometric function.
12
5
Given that sin = and cos = , find the exact values of each 13
13
of the remaining trigonometric functions.
step 1: Identify what information is given and what needs to be discovered
opp
= hyp
opp = 12
= adj
hyp
adj = 5
hyp = 13
step 2: Using this information, find the remaining trigonometric functions
=
csc =
sec =
cot = Feb 27 ­ 7:02 AM
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5.3 Day 1 Properties of Trigonometric Functions
March 02, 2009
Feb 27­9:26 AM
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5.3 Day 1 Properties of Trigonometric Functions
March 02, 2009
Finding the exact values of a trigonometric function.
, find the exact values of each of Ex. 1 Given that the remaining five trigonometric functions.
Step 1:
Determine the Quadrant the P(x,y) is in.
Step 2:
Draw a triangle in the appropriate quadrant.
Step 3:
Identify the given values x, y, or r.
Find the value of x.
Feb 27 ­ 7:02 AM
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5.3 Day 1 Properties of Trigonometric Functions
Step 4:
March 02, 2009
Find the remaining trigonometric values.
Feb 27 ­ 9:13 AM
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5.3 Day 1 Properties of Trigonometric Functions
Ex. 2
March 02, 2009
Given that find the other trig functions.
Feb 27 ­ 8:26 PM
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5.3 Day 1 Properties of Trigonometric Functions
March 02, 2009
HOMEWORK: page 399 (12 ­ 42 even)
Feb 26­11:38 AM
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