Math 10/11 Honors Section 3.6 Basic Trigonometric Identities
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1 Math 0/ Honors Section 3.6 Basic Trigonometric Identities SECTION 3.6 BASIC TRIGONOMETRIC IDENTITIES Copright all rights reserved to Homework Depot: I) WHAT IS A TRIGONOMETRIC IDENTITY? A trigonometric identit is an equation that is equal for all values of the variable(s) for which the equation is defined Eamples of trigonometric identities sin cos Trigonometric equations that are not Identities sin 0.5 II) ODD VS EVEN IDENTITIES: Even Identities: An function that looks the same when reflected over the -ais (Horizontal Reflection) Odd Identities: A function that looks the same when reflected over both the X and Y ais Copright all rights reserved to Homework Depot:
2 Math 0/ Honors Section 3.6 Basic Trigonometric Identities III) PYTHAGOREAN IDENTITIES: Review: The coordinates of an point on the circumference of an unit circle can be represented b: P, cos sin Other Pthagorean Identities can be generated b dividing all terms b either cos or sin IV) BASIC IDENTITIES Odd- Even Identities Reciprocal Identities Quotient Identities Pthagorean Identities V) VERIFYING AND PROVING IDENTITIES There are two was to Verif an identit Plug variet of numbers into the equation If the equation is equal for all the values, then the equation is an identit OR Graph the equations, if the completel overlap, then it s an identit Proving an Identit Simplif the equation algebraicall and then show that both sides are equal When proving algebraicall, first convert all functions into sine or cosine Then simplif using basic identities Copright all rights reserved to Homework depot: Copright all rights reserved to Homework Depot:
3 Math 0/ Honors Section 3.6 Basic Trigonometric Identities EX: VERIFY THE FOLLOWING IDENTITY: i) sin sec tan PRACTICE: VERIFY THE FOLLOWING IDENTITIES NUMERICALLY: sin sec cos tan ii) sin cos tan PRACTICE: VERIFY EACH OF THE FOLLOWING IDENTITIES: sin sin cot sin cot cos sec Copright all rights reserved to Homework Depot: 3
4 Math 0/ Honors Section 3.6 Basic Trigonometric Identities VI) PROVING IDENTITIES ALGEBRAICALLY: When proving trigonometric identities: Convert all trig. functions to sine or cosine Use basic trig. Identities to simplif complicated ones Odd/Even, Quotient, Pthagorean Identities Start with the side that looks more complicated You ma need to rationalize the epression, factor out common factors, or multipl all terms b the LCD Trial and Error (Do whatever it takes) Once the left side and right side are equal then the equation is a trigonometric identit VII) PROVING TRIGONOMETRIC IDENTITIES BY USING BASIC IDENTITIES: tan cos sin sec tan sin Left Side Right Side Left Side Right Side VIII) PROVING BY ADDING/SUBTRACTING IDENTITIES sin cos sec sin cos Copright all rights reserved to Homework Depot: 4
5 Math 0/ Honors Section 3.6 Basic Trigonometric Identities PRACTICE: PROVE THE FOLLOWING IDENTITIES: cos sin sin ta n cot sec tan sin cos cos IX) PROVING IDENTITIES USING FRACTIONS : tan sec tan csc Left Side Right Side X) PROVING IDENTITIES BY FACTORING: 4 sin sin cos sec 4 cos Copright all rights reserved to Homework Depot: 5
6 Math 0/ Honors Section 3.6 Basic Trigonometric Identities PRACTICE: PROVE THE FOLLOWING IDENTITIES BY FACTORING 4 sec tan tan cot csc cot XI) PROVE BY CONJUGATING THE EXPRESSION: sin cos Quotient Identities cos sin sin tan cos Reciprocal Identit cos cot csc sin sin sec cos Pthagorean Identit sin cos tan sec cot csc Formula Sheet Copright all rights reserved to Homework depot: PRACTICE: PROVE THE FOLLOWING IDENTITY BY CONJUGATING THE EXPRESSION: Formula Sheet cot csc csc cot Quotient Identities sin tan cos Reciprocal Identit cos cot csc sin sin sec cos Pthagorean Identit sin cos tan sec cot csc CLOSE Copright all rights reserved to Homework depot: Copright all rights reserved to Homework Depot: 6
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