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.
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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.
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Find the exact value of the following trigonometric functions.
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Signs of your function depend on which quadrant you are in.
cosine is negative
sine is positive
cosine is negative
sine is negative
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cosine is positive
sine is positive
(­ , +)
(+ , +)
(­ , ­)
(+ , ­)
cosine is positive
sine is negative
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
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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 = 5
adj
hyp
hyp = 13
step 2: Using this information, find the remaining trigonometric functions
=
csc =
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sec =
cot = 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.
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Step 4:
Find the remaining trigonometric values.
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Ex. 2
Given that find the other trig functions.
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HOMEWORK: page 399 (12 ­ 42 even)
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