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6.6 Trig Equations & Inequalities in Quadratic Form

6.6 Trig Equations & Inequalities in Quadratic Form. – 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

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6.6 Trig Equations & Inequalities in Quadratic Form

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  1. 6.6 Trig Equations & Inequalities in Quadratic Form

  2. – 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

  3. Ex 2) Solve

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

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

  6. 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) Press Mode Arrow down to 3rd line (Radian / Degree) Arrow right to put cursor over Degree & hit enter Put in graphing calculator by Press Y = button On line Y1, enter: 2sin(x)2 – cos(x) – 1 Press Zoom button Press 7: ZTrig for Zoom Trig make sure to put in the )

  7. 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 2nd 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!! • & Hit ENTER • Calc says X = 60 Y = 0 • Calc says X = 300 Y = 0 Sketch the graph & label!

  8. 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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