5.3 solving trigonometric equations. what are two values of x between 0 and when cos x = ½ x =...
TRANSCRIPT
Why does this work?
Look at the Cosine function, there are many times it equals ½
We limited it to 0 to
2
1,
3
2
1,
3
5
2
Set each factor equal to 0
Solve ( remember the period for tan is )
nx
x
0
0tan
3
3tan
3
1tan
1tan3
01tan3
2
2
2
x
x
x
x
Set each factor equal to 0
Solve ( remember the period for tan is )
nx
x
x
0
0arctan
0tan
3
3tan
3
1tan
1tan3
01tan3
2
2
2
x
x
x
x
n
n
6
5
3
3arctan
63
3arctan
When solving a trig equation, you must have only one function
Solve for x where the domain is )2,0[
2tansincos xxx
When solving a trig equation, you must have only one function
Solve for x where the domain is )2,0[
2cos
sinsincos
2tansincos
x
xxx
xxx
When solving a trig equation, you must have only one function
Solve for x where the domain is )2,0[
2cos
sin
cos
cos
2cos
sinsincos
2tansincos
22
x
x
x
x
x
xxx
xxx
When solving a trig equation, you must have only one function
Solve for x where the domain is )2,0[
2cos
sincos
2cos
sin
cos
cos
2cos
sinsincos
2tansincos
22
22
x
xx
x
x
x
x
x
xxx
xxx
When solving a trig equation, you must have only one function
Solve for x where the domain is )2,0[
2cos
sincos
2cos
sin
cos
cos
2cos
sinsincos
2tansincos
22
22
x
xx
x
x
x
x
x
xxx
xxx
xx
cos2
1;2
cos
1
When solving a trig equation, you must have only one function
Solve for x where the domain is )2,0[
2cos
sincos
2cos
sin
cos
cos
2cos
sinsincos
2tansincos
22
22
x
xx
x
x
x
x
x
xxx
xxx
3
5,
3;
2
1arccos
cos2
1;2
cos
1
xx
xx
Solve for x
Let 2x = u
3
5,
3
2
1cos
2
12cos
u
u
x
26
5;2
6
6
5
2
1
3
5;
3
52
62
1
3;
32
nxnxSo
xx
xx
Solve for y: Domain
Let sin y = u
01334
0341343
034912
031312
03sin13sin12
2
2
2
uu
uuu
uuu
uu
yy
)2,0[
Solve for y Range
Let sin y = u
01334
0341343
034912
031312
03sin13sin12
2
2
2
uu
uuu
uuu
uu
yy
01sin33sin4 yy
y
y
y
y
4
3arcsin
4
3sin
3sin4
03sin4
Solve for y
Let sin y = u
01334
0341343
034912
031312
03sin13sin12
2
2
2
uu
uuu
uuu
uu
yy
01sin33sin4 yy
y
y
y
y
4
3arcsin
4
3sin
3sin4
03sin4
y
y
y
y
3
1arcsin
3
1sin
1sin3
01sin3
3398.0y 8481.0y
Solve for y: domain
We have to give all the answers
3398.0
8481.0
)2,0[
3
1
4
3 294.28481.0
803.2339.0
Homework Homework
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28, 35, 57,28, 35, 57,
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