'Sinx' diaporamas de présentation

???????

???????. ??????. ??. 1 ???. ? 1 ??? y=x 2 ???. ? 2 ??? y= ? x-2 ? 2 ? y= ? x+3 ? 2 ???. ??????????????. ???????? a ???? f ? x ??????? a ???? f ? x+a ???? f ? x ??????? a ???? f ? x-a ????. ??????????????. ?? y=x 2 ??????????.

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3.2 ?????

?????? 1-1. 3.2 ?????. y. x. o. ??????. (1) ??? f(x)=2 ????. (2) ??? f(x)=0 ????. 0. (3) ??? f(x)=-2 ???. 0. ????????. (1) y=x ???. (2) y=x 2 ???. (3) y=x 3 ???. ???. (1) y=x 4 ;. (2) y=x -5 ;. -5x -6. 4x 3. -2x -3. ????? ,n ????. ? ? ?. ??????????????. ???? 5 ? !.

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???????

???????. ??? ???. MP. ???. ?????. ???. ???. ? ???. y. P. o. M. x. A (1,0). ?????. ?????? ????. ?. y. P. x. A (1,0). M. O. ???? MP. y. P. x. A (1,0). M. o. ???? MP. y. ?. P. x. o. A (1,0). M. ????????. ????????. y. (B). B. 1. x. A. o. O 1. ?. ( A ).

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The Wave Function

The Wave Function. What is to be learned?. How the wave function tactic sorts out functions containing sine and cosine. Previously. Max value of 5sinx is Min value of 5sinx is . 5. -5. 5. -5. How about 7cosx + 5sinx. cos max at x = 0 0. sin max at x = 90 0. ?.

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??????????? ???? 4

??????????? ???? 4. ???? ??. ?? ?? y= sinx ??????. 1 ? y=sinx ??? ? x ? [0 ? 2?] ?. 2 ? y=sinx ???. ? ??? R ? ? ?? [-1 ? 1] ???? 1 ????? 1 ? ? ????? T ? 2? ? ? ?????????????????????. ? ????? [2k? ? 0.5? ? 2k? ? 0.5?] ??????

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??? ?????????????

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??????????

??????????. y. x. x. -1. O. ????? 1. ??????? ? ???????? , ?????????. ?????. ????. sin ?=MP. ??? MP. ???? ???? ????. cos ?=OM. ??? OM. tan ?=AT. ??? AT. T. P. ??? ?????? ???? ?. ?. A(1,0). M. ???. A(1,0). y. ????. ???. ??. o. x. T. P(x,y). 1. M. - 1. 1. - 1.

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?????????

?????????. ?????? ???? ? ?. 1. ???? y=sinx ??? y=Asinx(A>0) ? ???????? 2. ?? ?? y=sinx ??? y=sin ? x+ ?????????. ?????. ???. ???. ?? 1. ? 1. ???????? y=sinx ??? y=2sinx ??? y=1/2sinx ? ??????????????. ???? i ? ?? ii ? ??? iii ???. ???. ???.

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?????

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Starter

Starter. Draw the graph of y = log(x+1) for -6? x ? 14. Draw in the asymptote. Asymptote is at x = -1. Note 9 : Periodic Functions. Periodic Function A function that repeats itself over and over is a horizontal direction. Period of a Function

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5.3 Solving Trigonometric Equations

5.3 Solving Trigonometric Equations. *use standard algebraic techniques to solve trig equations *solve trig equations in quadratic form *solve trig equations with multiple angles *use inverse trig functions to solve trig equations. Review. Sine domain = all real numbers range = [-1, 1]

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Trig Identities

Trig Identities. What is to be learned?. Some new trig formulae Correct methodology and structure for proofs. =(Sinx) 2. Squaring Sinx Sinx X Sinx Written as sin 2 x. Some exciting calculations sin 2 (30) + cos 2 (30). (sin30) 2 + (cos30) 2. Repeat for 75.3 0.

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Note 2: Sine and Cosine Curve

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Trig Identities

Trig Identities. What is to be learned?. Some new trig formulae Correct methodology and structure for proofs. =(Sinx) 2. Squaring Sinx Sinx X Sinx Written as sin 2 x. Some exciting calculations sin 2 (30) + cos 2 (30). (sin30) 2 + (cos30) 2. Repeat for 75.3 0.

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???????

???????. ??????? y=sinx vs y=2sin(2x-1)+2. ??????? y=2sin(2x-1)+2 y= ? sinx. ??????? y=2sin(2x-1)+2 y= ? sinx+ 2. ??????? y=2sin(2x-1)+2 y=sinx vs y= 2 sinx(x- 1 )+ 2. ??????? y=2sin(2x-1)+2 y=sinx vs y= 2 sinx(x- 1 )+ 2. ??????? y=2sin(2x-1)+2 y=sinx vs y= 2 sinx( 2 x- 1 )+ 2.

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Derivatives and Inverse Functions

Derivatives and Inverse Functions. 1. Complete the table (without a calculator) for f(x) = sinx 2. Convert both the x- and y- values from your table to the nearest tenth. 3. Use the tables above to produce a table for f -1 (x) = arcsinx

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