Download Unit IXa: Trig III Solving More Difficult Trignometric Equations (8.5)

Solving Trignometric
Equations
6.2
JMerrill, 2009
Solving an algebraic
equation
x  3x  4  0
( x  1)( x  4)  0
2
( x  1)  0 or ( x  4)  0
x  1
x4
Solving a Trigonometric
Equation Using Algebra
Solve 2sin   1  0 for 0    360
2
2sin   1  0
2
2sin   1
2
1
sin  
2
2
2
sin   
2
o
o
There are 4 solutions
because sin is positive
in 2 quadrants and
negative in 2 quadrants.
  45o ,135o ,225o ,315o
Solve
sin x  sin x  cos x
2
2
Hint: Make the words match
sin x  sin x  1  sin x
2
2
sin x  sin x  1  sin x  0
2
2
2sin x  sin x  1  0
2
Quadratic: Set = 0
Combine like terms
Factor—(same as 2x2-x-1)
(2sin x  1)(sin x  1)  0
1
sin x 
or sin x  1
2
x
 7 11
,
2 6
,
6
Solve
Solve sin x tan x  3sin x for 0  x  2
sin x tan x  3sin x  0
Round to nearest
hundredth
sin x(tan x  3)  0
sin x  0
or tan x  3
x  0,3.14
x  1.25,4.39
Where did these 2 answers
come from??? 
Solve
Solve 2sin  cos for 0    360
o
2sin  cos
cos
2
sin 
o
2  cot 
1
 tan 
2
  26.6 ,206.6
o
o
What You CANNOT Do
• You cannot divide both sides by a
common factor, if the factor cancels
out. You will lose a root…
Example
sin x tan x  3sin x
sin x tan x 3sin x

sin x
sin x
tan x  3
Common factor—
lost a root
2sin  cos
cos
2
sin 
2  cot 
1
 tan 
2
No common factor = OK
You Do
• Solve 2cos2 x  cos x  1  0 on 0  x  2
2cos x  1cos x  1  0
1
cos x  or cos x  1
2
 5
x ,
3 3
Check by graphing!
x