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Solving Trigonometric
Equations
Single Variable
FUNCTIONS OF THE SUM
OF TWO ANGLES
Sin(A+B) = sinA cosB + cosA sinB
Cos(A+B) = cosA cosB – sinA sinB
FUNCTIONS OF THE
DIFFERENCE OF TWO
ANGLES
Sin(A-B) = sinA cosB – cosA sinB
Cos(A-B) = cosA cosB – sinA sinB
LAW OF SINES
a
b
c


sin A
sin B
sin C
FUNCTIONS OF THE HALF
ANGLE
1
1  cos A
sin A  
2
2
1
1  cos A
cos A  
2
2
Solve 4 cos x + 1 = -1









A. ISOLATE COS X
4 COS X = -2
COS X = -1/2
B. FIND REFERENCE ANGLE
REF ANGLE=60o
C. DETERMINE QUADRANTS
QUADRANTS: II,III
D. FIND ANGLE IN CORRECT
QUADRANTS
X = 120o, 240o
Solve 4 tan2 x = 1
• 4 tan2x = 1
•
2
tan x
=¼
• tan x = +1/2, -1/2
•reference angle=
26.56505118=26o33’54.184”
•Quadrants: ALL
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