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Trig 3.1: Trigonometric Identities

Trig 3.1: Trigonometric Identities. Definitions : Conditional equation —a statement that is true for a specific set of values Identity —an equation that is true for all real #’s in the domain. Fundamental Identities: 1. Reciprocal Identities:. 2. Quotient Identities:.

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Trig 3.1: Trigonometric Identities

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  1. Trig 3.1: Trigonometric Identities • Definitions: • Conditional equation—a statement that is true for a specific set of values • Identity—an equation that is true for all real #’s in the domain • Fundamental Identities: • 1. Reciprocal Identities:

  2. 2. Quotient Identities: 3. Pythagorean Identities: 4. Cofunction identities:

  3. 5. Even-Odd Identities: Even: Odd:

  4. C. To simplify a trig expression, use algebra and these identities 1. Factoring: 1. Factor sec2 x – 1 2. Factor 4 tan2 x + tan x – 3 3. Factor csc2 x – cot x – 3 2. Complete: 4. sin x + cot x cos x 5. tan2 x sec2 x – tan2 x

  5. Trig 3.2: Proving Identities A. Guidelines for Establishing Identities: 1. Work on one side of equation at a time 2. Look to factor, add fractions (LCD), use FOIL, or create a monomial denominator 3. Look to use fundamental identities 4. Perhaps try to convert all terms to sin and cos 5. Try something!!

  6. Trig 3.3: Trigonometric Equations A. To Solve a Trig Equation: 1. Use algebra to isolate the trig function 2. Find the reference angle 3. Determine which quadrants is in on the interval 4. List solution(s)

  7. B. To solve quadratic trig equations: 1. Use factoring and other algebra techniques to isolate functions 2. Substitute using identities if necessary 3. Solve over

  8. Trig 3.4: Using Calculators A. Finding inverse functions using calculator: 1. Use 2ndsin-1, cos-1, tan-1 when trying to find an inverse function 2. Be sure calculator is in RADIAN mode 3. For cot-1, sec-1, csc-1 use the reciprocal of x <check quadrants carefully for cot-1 !!>

  9. B. Solving trig equations -- calculator problem guidelines: 1. Use 2ndinverse function to determine the reference angle 2. Round to 3 decimal places 3. RADIAN mode 4. Use coterminal angles to list all solutions

  10. Trig 3.5: Sum & Difference Formulas • Formulas for cosine: • Formulas for sine: • C. Formulas for tangent:

  11. A. Double Angle Formulas: Trig 3.6: Double-Angle & Half-Angle Formulas

  12. B. Half-Angle Formulas:

  13. Trigonometry Unit 3 Test • Grademaster #1-30 (Name, Date, Subject, Period, Test Copy #) • Do Not Write on Test! Show All Work on Scratch Paper! • Label BONUS QUESTIONS Clearly on Notebook Paper. (If you have time) • Find Something QUIET To Do When Finished!

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