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## 4.5 (Day 2) Inverse Sine & Cosine Graphs

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**We learned before about the inverse sine & cosine functions**and how their domains need to be restricted. Let’s see why graphically. y = sin x If we simply reflected over y = x we get NOT a function**Go back to y = sin x & restrict its domain**- want non-repeating values - want positive & negative values Take your paper and trace over the x- & y-axis and the tick marks in Sharpie. Now trace just the part of the curve from Add (+) signs where x-axis & y-axis are positives. Now reflect your paper over y = x. Are (+) in right spots? This is y = Sin–1 x + positive + negative**Let’s label!**y = Sin–1 x + Check that points are the inverse of points of original sine inversesine + –1 1 YES!! Let’s do the same with cosine, but faster this time! **y = cosx**reflect over y = x NOT a function Restrict the domain Want positive & negative & no repeats + positive Take WS & trace axes, tick marks, & section of curve from 0 to π Label positive parts of x- & y-axes + negative**Reflect paper (turn it over)**Put positives in right places Label your new picture y = Cos–1 x Check that points are the inverse of points of original cosine inversecosine + (0, 1) (1, 0) (–1, π) YES!! + (–1, π) (π, –1) –1 1 (1, 0)**Now let’s transform Cos–1x and Sin–1x**a, b, c, & d still have same effects as before with sin & cos y = a Cos–1b(x – c) + d and y = a Sin–1b(x – c) + d Ex 1) y = Sin–1x + 2 up 2**Ex 2) y = 2Sin–1x**stretch factor 2 (taller)**Ex 3) y = –Cos–1x**flip over x-axis**Ex 4) y = Cos–1 (½ x)**b = ½ “period” wider**Homework**#406 Pg 220 #20, 21, 32, 34, 35 & Pg 213 Test Yourself (all)