1. Bearing Complex Polar Coordinates Binomial Theorem (Terms) Trig Equations Law of Cosines Binomial Theorem (Basic) Vectors SSA Triangles Comments Please report any errors ASAP by email to sakim@fjuhsd.net or IM at kimtroymath.sakim@fjuhsd.net Problems may be more difficult on test. Consult homework assignment. Not all topics covered. Ones in read are the ones that have been completed. Remember, some material is on other powerpoints. Green are always changing.

2. 1) Figure out angles 2) Make vectors 3) Add vectors 4) Find magnitude 5) Find Bearing A plane is traveling 400 miles per hour west. A wind from a direction of N 60 o W is 10 mph. Find the ground speed and bearing of the plane. (I will round to hundredths) 180 o Wind is coming FROM this direction, which is different from where it is heading. 60 o So it’s really heading E 30 o S. 330 o Distribute the magnitude. Remember, magnitude is the same as ground speed. Remember inverse tangent is either quadrant I or IV. Make a sketch of the vector to see what quadrant the angle is supposed to be in. QI  NothingQII  Add 180QIII  Add 180 QIV  Add 360 Then find the bearing afterwards. QIII The angle for the bearing is.73. You can either subtract 180, or logically deduce it, or whatever you may need. You don’t always subtract 180. It depends on what quadrant it’s in. Read problems carefully, whether the wind is coming FROM a direction or is HEADING IN A direction. Heading in a direction is straight forward, coming from a direction is trickier.

3. Putting into complex polar coordinate form. 1) Find radius 2) Find argument (angle) a) Inverse Tangent b) Figure out angle i) QII, QIII add 180 ii) QIV, add 360 Convert the other complex number into complex polar form. Next click will give answer.

4. Binomial Theorem Common errors: 1) Parenthesis, you need them. Otherwise your powers will be messed up. (Math kryptonite) 2) Set up the bottom factorial carefully. 3) Keep sign. Notice: 1) First term starts with exponent, goes down by 1. 2) Second term starts with 0, goes up by 1. 3) Bottom number matches up with second term exponent. 4) Exponents add up to n 5) Term number is ONE MORE than bottom number. 1 st term 2 nd term 3 rd term 4 th term

5. Binomial Theorem (Terms) Methods 1) Be safe, list them all, pick the one you need 2) Logic 3) Formula List Clear Logic Clear Formula Clear 1) Bottom number matches up with second term exponent. 2) Exponents add up to n 3) Term number is one more than bottom number. The rest, you use logic to set it up so that you can use the formula. Refer to other slide or logic button for logical rules. You use logic to set up the x term.

7. Check the General Trig Powerpoint Ch 6 for good equation examples. If you want a specific hw problem done, e-mail me. I’ll try to fit 1 or 2 in here.

8. Law of Cosines – To be used with SSS or SAS triangle. There are no ambiguous cases for these triangles. SSS – 3 sides givenSAS – 2 sides given, name of angle is not the letter of the other sides. (or make a sketch) Quick Check, small angle small side, middle angle middle side, big angle big side. CHECK MODE OF CALCULATOR! Just showing LOC step. Use LOS to finish the problem. A B C b a c A B C b a c

9. SSA triangle. Use law of sines. Rules h = bsinA a is the side opposite the angle. b is side adjacent to angle a < h, no triangle a = h, one right triangle a < b and h < a, 2 triangles a ≥ b, one triangle A b a A A A a a a a b b b You can use common sense. Set up a law of sines. And then try to find the supplement. See if 0, 1, or both triangles work. Common sense is nice because even if you use the rules, if you notice there are 2 triangles, you will need to use the supplement anyways. m A = 40 o ; a = 4, b = 5 5 40 o 4 4 5 53.46 o Check supplement and the third angle. 180-53.46 o = 126.54 o 126.54 o 86.54 o 13.46 o Both triangles are ok, you can finish using law of sines. m C = 30 o ; c = 6, b = 4 6 30 o 4 6 4 19.47 o Check supplement and the third angle. 180-19.47 o = 160.53 o 160.53 o 130.53 o -10.53 o 2 nd triangle is impossible, only need to solve for the top one.

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15. Comments Make sure you really understand graphing and solving equations. Graphing, know the formulas, and how to find period, amplitude and shift.