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6.6 Trig Equations & Inequalities in Quadratic Form

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– Quadratics can be solved by factoring or using the quadratic formula – Now “x” will be a trig function we must deal with & solve for at the end – Note: To solve, it should have the same trig functions Find exact solutions if possible, and if not, round to nearest hundredth in radians. Ex 1) Solve but… there were no restrictions so we have to consider all answers

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Ex 2) Solve

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Ex 3) Solve (not famous angles) x = 0.46 or 0.46 + π = 3.60 x = –1.11 –1.11 + 2π or –1.11 + π = 5.17 = 2.03 0.46, 2.03, 3.60, 5.17

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Ex 4) Solve can’t factor it, so use quadratic formula a = 1, b = 1, c = 1 only imaginary answers so No Solution

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Ex 5) Use a graphing calculator to find the solution of on [0, 2π). Sketch the graph obtained by your calculator Set equation ≥ 0 Let’s put the calc in Degree mode (then we’ll change our answer to rads) 1)Press Mode 2)Arrow down to 3 rd line (Radian / Degree) 3)Arrow right to put cursor over Degree & hit enter Put in graphing calculator by 1)Press Y = button 2)On line Y1, enter: 2sin(x) 2 – cos(x) – 1 3)Press Zoom button 4)Press 7: ZTrig for Zoom Trig make sure to put in the )

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Ex 5) cont… We want the x-values from 0 to 2π for when the graph is above the x-axis (that’s when it’s ≥ 0) Now press the 2 nd Trace button to get CALC Press 2: zero Use right arrow to move cursor over to left of here Use right arrow to move cursor over to right of there & hit ENTER Hit ENTER again Do the same thing for here So the graph is above the x-axis between 60° and 300° Change to radians!! Sketch the graph & label! Calc says X = 60 Y = 0 Calc says X = 300 Y = 0 & Hit ENTER

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Homework #605 Pg 321 #1–13 odd, 17, 19, 23, 25, 27, 30, 39 Sketch the graph you get from your calc for #17, 19, 39 Even Answers: #30:

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