Solving Trig Equations Objective: Solve many different Trig equations.
18 Days. Four days We will be using fundamental trig identities from chapter 5 and algebraic...
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Transcript of 18 Days. Four days We will be using fundamental trig identities from chapter 5 and algebraic...
Chapter 6 – Analytic Trigonometry
18 Days
6.1 – Verifying Trigonometric
IdentitiesFour days
We will be using fundamental trig identities from chapter 5 and algebraic manipulations to verify complex trig equations are in fact identities.
If both sides of an equation are exactly equal for all values of x then we call the equation an identity.
You should review the trig identities that we have previously covered so they are fresh in your mind.
Verifying Trig Identities
1. You must show ALL your steps.2. You may only work with one side.3. Look for chances to factor, combine
fractions, multiple by conjugates, etc.4. Look for chances to substitute trig identities.5. If all else fails, re-write the entire equation
in terms of sine and cosine.6. Don’t just stare at an identity. Try
something, there are often several ways to verify most identities.
Rules (Guidelines) for Verifying Identities
Verify the Identity - Example 1
1cottan xx
Verify the Identity - Example 2
22
2
sinsec
1sec
Verify the Identity - Example 3
xxxx 32 sinsincossin
Verify the Identity - Example 4 xxx 222 tan1cos1tan
Verify the Identity - Example 5
xxxx
sectansecsin1
1 2
Verify the Identity - Example 6
xx
x
x
xcot
cos
sin
sin
sec
Verify the Identity - Example 7
y
yyy
sin1
costansec
Verify the Identity - Example 8
sin
sin1
csc1
cot2
Verify the Identity - Example 9
csc
tansin
sec1
p456 #1,3,4,6,8, 9,13
Homework
p456 #14,16,17,21 - 25
Homework
Trig identities worksheet #1 - 10
Homework
p24 Prentice Hall paper do #5 - 8, 10 - 13, 17 - 19(17 - 19 not on quiz)
Homework
6.2 Trigonometric Equations
Four Days
Find the solutions of
if θ is on the interval [0,2π).
if θ is any real number.
Solving Trig Equations
21cos
Find the solutions of
Solving Trig Equations
1tan
Find the solutions of
Solving Trig Equations
232sin
Find the solutions of
Solving Trig Equations
02cos21sin2 xx
Find the solutions of
Solving Trig Equations
0cos3
p469 #1,2,4,6,7,10,19 - 23, 25,27, 30,31,33 solve for interval [0,2π)
Homework
Solving Trig Equations - Day 2
Find the solutions of
Solving Trig Equations - Day 2
tt sin1sin2 2
Find the solutions of
Solving Trig Equationsxxx sinsintan2
Find the solutions of
Solving Trig Equations sec1tan
Find the solutions of
Solving Trig Equations1cossin3 tt
HW: p469 #34,39,40,42,45,47,51,53,57,58,60,61,63
Homework
6.3 The Addition and Subtraction Formulas
Three Days
Sometimes it is possible to find trig values that are not on the unit circle if we can write them as a sum or difference of unit circle values◦ Cos(165o)=Cos(120o+45o)
Note: cos(x+y) is NOT the same as cos(x)+cos(y). We will have formulas to help us simplify these expressions.
Sum and Difference Identities
Sum and Difference Identities
Find cos(105o)
Find tan (-285o)
Find cos(110o)cos(20o)+sin(110o)sin(20o)
Sum and Difference Examples
7-3 Sum and difference Identity worksheet Skip #5,8,10
Homework
Cofunction Identities
Express the following as a cofunction of a complimentary angle
103
41
2
43
sec
sin
cos
tan
115sin
p480 #1, 7, 11,13, 17 D 27odd,32,41
Homework
6.4 Multiple Angle Formulas
Two Days
Double Angle Formulas
Example – Solve the following
02sincos2 xx
More Examples
2tan and 2cos 2sin Find
and sinGiven 2135
Glencoe 7.5 skip #4 & 13
Homework
6.4.2
More Practice with Multiple Angles
Verify the Identity 2cot2tancot
Re-write as a single angle
x3sin
Solve 1sinsin 33 xx
p490 #1,4,11,14,15,33 - 37
Homework