Download Solving Trigonometric Equations

Solving Trigonometric Equations
Ashley Cleaton, Levi Hoffman, Anna Slominski
Goal of solving the trig equations is to isolate the triq
function, then use the inverse function to find your answer.
Procedures:
1.
Solving Linear Equations
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Isolate the Trig function
Use the Inverse to Find Answer
2. Solving Quadratic Equations
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Move all variables and numbers to one side
Factor into two parts
Set factors equal to zero
Solve each equation
If not factorable then use quadratic formula
X + X = 2X
You can use factoring, collecting
like terms, square roots, rewriting
the equation with a single function,
and inverse function to find your
answer.
Solve By Isolation
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Use math operations to get the function by itself
Use inverse function to find finale answer
Ex:tanX=1
X=tan-1(1)
X= /4, 5 /4
Solve
√3tanX=1
Solve by Isolation and Inverse
Ex. √3 tanX=1
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tanX= 1/√3
tanX= √3/3
X= arctan(√3/3)
X= /6, 7 /6
Solve by Combining like Terms
● Use math operations to get all constants and function on
the same side
● Combine like terms
● Solve using inverse
● Solve
● sinX+√2=-sinX
Solve by Combining like terms and Inverse
Ex: SinX + √2 = -sinX
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Sinx + Sinx + √2 = 0
2SinX + √2 = 0
2SinX = -√2
Sinx = -√2/2
X= arcsin (-√2/2)
X= 5 /4, 7 /4
Solve by extracting the Square root
● Use math operations to get the function by itself
● Square root both sides to get rid of the square on the
function
● Remember that square rooting makes it positive and
negative
● Solve using the inverse
● Solve
● 3tan2X-1=0
Solve by Extracting Square Root
Ex: 3tan2X -1= 0
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3tan2X=1
tan2X= ⅓
tanX= 1/√3
tanX=√3/3
X=tan-1(√3/3)
X= /6, 7 /6, 5 /6, 11 /6
Solve by Factoring Linear Equations
● Get the variables and constants on to the same side(make
the equation equal zero
● Distribute out the LCM which should be a variable
● Set both factors equal to zero
● Solve each individualy
● Solve
● cotXcos2X=2cotX
Solve Quadratics by Factoring
Ex: cotXcos2X=2cotX
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cotXcos2X-2cotX=0
cotX(cos2X-2)=0
cotX=0
cos2X-2=0
X= , 0
cosX=√2
X=cos-1(√2
Solve by Factoring Quadratic Equations
● Using math operations get all functions and constant on the
same side
● Factor out so equation is in two pieces
● Set both parts equal to zero
● Solve each equation separately
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Solve by Rewriting using One Function
● Using math operations get all constants and functions on
the same side
● Change one of the functions to be the same as the other
● Ex: sin2X+2cos2X
1-cos2X+2cos2X
● Solve using factoring
● Solve
● 2sin2X+3cosX=0
Solving Quadratics by Rewriting and Factoring
Ex:
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2(sin2X)+3cosX=0
2(1-cos2X)+3cos=0
2-2cos2X+3cos=0
2cos2X-3cosX-2=0
(2cosX+1)(cosX-2)=0
cosX=½ cosX=2
X=cos-1(½) X=cos-1(2)
X= /3, 5 /3 X=none
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Additional Examples
2sinX-1=0
tan2X-3=0
2cos2X=√3cosX
sinX+cosX=1
2secX+1=0