Trigonometric Equations Section 10'3

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Trigonometric Equations Section 10.3

• Juveria Nayeem
• Chris Williams
• Kristine Randolph

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Basic Algebraic Techniques

• Introduction
• To solve a trigonometric equation, use standard
  algebraic technique such as like terms and
  factors.
• The Best way to understand the equations is to
  start off with basic algebra rules
• For example
• PLEASE EXCUSE MY DEAR AUNT SALLY
• PParentheses (x)
• EExponents
• MMultiply 1 2 2
• D Divide ¾
• AAdd 246
• SSubtract 4-22

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Unit Circle

• (X,Y) (Cosine, Sine)
• For example
• Sin30 1/2
• How was this possible
• 1.Locate 30 on unit circle
• 2.State the coordinates
• ( , )
• 3.Pick the Sine
• (Cos,SIN)
• 4.Sin of 30 is

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Examples

• ex. 1
• Cos 150
• 1.Locate angle
• 2.State the coordinates (- , ½)
• 3.Narrow it down to cosine (COSINE,sine)
• ANSWER Cos 150 -
• ex.2
• Tan 315
• 1.Locate angle on unit circle
• 2.State coordinates ( ,- )
• 3.If Tansine/cosine..so
• 4. ANSWER -1

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Examples

• Now lets work backwards
• Ex.a
• Sin x
• 1.Look on the unit circle for radians, that
  coorespond with the Sine of
• 2. Locate and state itits that easy!! ?
• 3. There will be more than one answer.
• ANSWER X , and

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Examples

• Try for your self
• EX.b
• Tan x
• 1.Tan
• 2. Locate the y(sin), and x(cos) that correspond
• ANSWER 60 and 240

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Solving Trigonometric Equation

• Find all solutions of the equation
• Ex.1
• 2 sinx-10
• Solution
• 1.2 sinx-10 WRITE ORIGNIAL EQUATION
• 2. 2 sinx1 ADD ONE TO EACH SIDE
• 3. Sinx DIVIDE EACH SIDE BY 2
• To solve for x, sin x has solutions x and
  x

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Examples

• Solve the equation
• Ex. 2 cosx 10
• Ex. Tanx 0 Remember Tan

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Collecting Like Terms

• 1.Sin x -sin x
  1.Add Sin x to both sides
• 2.Subtract from each side
• 3.Combine like terms
• 4.Divide each side by 2

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Extracting Square Roots

• 3 Tan x-10 1. Add 1 to each side
• 2.Divide each side by 3
• 3. Extract square root
• Remember Tan x

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Factoring

• Cot x Cos x 2Cot x
• Sec x Csc x 2 Csc x

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Homework

• P. 645-646 7-17, 21,23, 27, 29 odd

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Helpful Website

• www.algebasics.com