Date Lesson Assignment Did it grade Friday Feb.24

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1 PAP Pre-Calculus Lesson Plans Unit Sem 2 3 rd term Johnston (C4) and Noonan (C6) February 24 th to March 9 th Vectors Date Lesson Assignment Did it grade Friday Feb.24 Law of Sines/Cosines, Area of a Triangle, Polynomial and Rational Functions WS on Law of Sines/Cosines, Area of a Triangle, Polynomial and Monday Feb. 27 Tuesday Feb. 28 Sect 6.3: Perform basic vector operations and represent them graphically TEXT/MATERIAL: Larson s Precalculus with Limits Precal - DA Rational Functions Pg 456: 3,6,9,,5,20-2,25, 27,32,34,39 and WS 2D Vectors Re-read Section 6.3 be prepared to use vectors in i-j form Wednesday Feb. 29 Thursday Mar. Friday Mar. 2 Monday Mar. 5 Sect 6.3: Perform basic vector operations and represent them graphically TEXT/MATERIAL: Larson s Precalculus with Limits Sect 6.3: Perform basic vector operations and represent them graphically Quiz #7 Basic Vector operations and Triangle Apps Sect 6.4: Dot Product of Vectors, Sum of component vectors TEXT/MATERIAL: Larson s Precalculus with Limits Pg 457: odds, 66, 67 WS 6.3 Pg. 467: 55 odds Vectors to solve Navigation Problems Navigation WS # Tuesday Mar. 6 Wednesday Mar. 7 Thursday Mar. 8 Friday Mar. 9 Vectors to solve Navigation Problems Quiz #8 Geometric Vectors and Dot Products TAKS - ELA Review for Test #4 - Vectors Test #4 - Vectors Navigation WS #2 and Supplemental problems for review Complete Navigation WSs Study for Test Review for Test #3.4 Unit

2 Area of a Triangle Right Triangle Trig K bcsin A 2 sin opposite hypotenuese K a 2 sin B sin C 2sin A cos adjacent hypotenuese K s( s a)( s b)( s c) a b c where s 2 tan opposite adjacent Triangle Formulas Law of Sines: sin A sin B sin C a b c Law of Cosines: a b c 2bc cos A Area of a Sector As 2 As r 2 is in radians 2 r 2 80 is in degrees Arc Length s r is in radians Other Trig Functions sec csc cot cos sin tan

3 Friday, February 24, 202 PRECALCULUS GT/HONORS REVIEW OF TRIANGLES Draw a figure for each problem. Show all work, and give your answers correct to three decimal places.. c 36, d 22, C 90. D 2. A 44, B 6, b 70. a = 3. P 08, q 54, r 66. p 4. P 87, Q 70, t 2. p = 5. m 20, k 2, l 9. K 6. D 8, d, e 5. E

4 7. Find the area of ABC given C 43, a 25, b Find the area of JKM given j = 8, k = 23, m = A surveyor measures the three sides of a triangular field and gets measurements of 0 m, 35 m, and 224 m. What is the measure of the smallest angle of the triangle? 0. Observers at point C and D, 72 km apart, spot an airplane Airplane overhead at angles of elevation of 42 and 56 respectively. How far is the plane from the observer at point C? C D. A ramp 8 m long makes a 24 angle with the horizontal. The ramp is to be replaced by a new ramp whose angle of inclination is only 5. How long will the new ramp be? New Ramp 5 24 Old Ramp 2. A ship is 5 miles from one radio transmitter and Ship 40 miles from another transmitter. If the angle between the signals is 32, how far apart are the transmitters? Transmitter Transmitter

5 Monday, February 27, 202 Notes 2-D vectors:. 2a Find the magnitude and the resultant. a 2. 2b b c 3. 4 a c 4. b c 5. a c b

6 Precalculus Name 2-D Vectors Worksheet # Date Period Draw the resultant and determine its magnitude.. 4b 2. w a b v a w a 3. 3 a 4. 4 b 5. 5v 6. a b 7. 3b v 8. 2v w 9. w b 0. a b v. w a b 2. a b 3 2

7 Wednesday, February 29, 202 Notes: Vectors - Finding the Magnitude and Direction Notes: Algebraic Representation Given: v means vector v 60 v 4cm w 75 w 0cm u 35 u 6cm Find the magnitude and direction of each resultant below: (Round answers to the nearest thousandth of a degree): v w w u.) v w 2.) w u 3) v u 4.) 2w u v u 2 w u

8 Thursday, March, 202 Notes/Examples of Geometric Vectors and Parallelograms/Triangles I. Look at the parallelogram below. Given: each of the following in terms of x and y. BC x CD y and P is the midpoint of AC and BD, find B C P A D. AD = 2. AB = 3. BA = 4. BD = 5. CB = 6. BP = 7. CA = 8. PA = 9. PC = II: In ABC, x and y. AP PB 3 PQ and. QC 4 A If PQ x and QB y, express the following in terms of P Q B C 0. BP =. PC = 2. BC = 3. AP = 4. PA = 5. AB = 6. AC = 7. BA =

9 Monday, March 5, 202 Navigation Examples Ex. A ship sails 00 km east, followed by 40 km along a bearing of 20. How far is the ship from its starting point? What is the bearing of the ship from its starting point? Ex. An airplane flies 240 miles on a bearing of 25 and then turns and flies 60 miles along a bearing of 30. How far is the plane from its starting point? What is the bearing of the plane from its starting point? Ex. An airplane is traveling in the direction 200 with an airspeed of 250 mi/h. There is a 35 mi-per-hour wind with a direction 285. Find the plane s ground speed and course. Ex. A plane is traveling in the direction 60 with an airspeed of 400 mi/h. Its course and ground speed are 45 and 385 mi/h respectively. What is the direction and speed of the wind?

10 PRECALCULUS GTIH VECTOR WORKSHEET _/ Work the following on notebook paper. Give decimal answers correct to three decimal places.. Forces of 34 pounds and 46 pounds make an angle of 42 with each other and are applied to an object at the same point. Find the magnitude of the resultant force. 2. Joe Jamoke and Ivan Hoe are pulling up a tree stump. Joe can pull with a force of200 pounds and Ivan with a force 0[250 pounds. A total force of 400 pounds is sufficient to pull up the stump. (a) If they pull at an angle of 25 to each other, will the sum of their force vectors be enough to pull up the stump? What is the sum of their force vectors? (b) At what angle must they pull in order to exert exactly the 400 pounds needed to pull up the stump?.. 3. Freda Pulliam and Yank Hardy are on opposite sides of a canal, pulling a barge with tow ropes. Freda exerts a force of 50 pounds at an angle of 20 to the canal, and Yank pulls at an angle of 5 with just enough force so that the resultant force vector is directly along the canal. Find the number of pounds with which Yank must pull and the magnitude of the resultant vector. Freda Yank 4. Aloha Airlines Flight 007 is approaching Kahului Airport at an altitude of 5 km. The angle of depression from the plane to the airport is 9 32'.. (a) What is the plane's ground distance from the airport? (b) If the plane descends directly along the line of sight, how far will it travel along this line in reaching the airport? Flight 007 ~ -==:---r-::--;-~ Airport 5. An airplane has an airspeed of 450 rni/h and a heading of 0. The wind is blowing from the east at 23 miih. Find the ground speed of the plane and its course. 6. A boat travels at 5 milh on a compass heading of 200. The velocity of the current is 3 mjh toward the north. Find the speed of the boat relative to land, and findits course. 7. An airplane is flying through the air at a speed of 500 kmih. At the same time, the air is moving with respect to the ground at an angle of 23 to the plane's path through the air with a speed of 40 km/h (i.e., the wind speed is 40 km/h). The plane's ground speed is the magnitude of the vector sum of the plane's velocity and the air's velocity with respect to the ground. Find the plane's ground speed ifit is flying: (a) Against the wind (b) With the wind TURN-»>

11 North 8. A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 57, as shown in the figure. (A knot is a nautical mile per hour, or slightly faster than a regular mile per hour.) The current has a velocity of 5 knots along a bearing of 23. The actual velocity of the ship is the vector sum ofthe ship's velocity and the water's velocity. Find the actual velocity. s 9. A navigator on an airplane knows that the plane's velocity through the air is 250 kmlh on a bearing of 237. By observing the motion of the plane's shadow across the ground, she finds to her surprise that the plane's ground speed is only 52 kmih, and its direction is along a bearing of 5. She realizes that ground velocity is the vector sum of the plane's air velocity and the velocity of the wind. What wind velocity would account for the observed ground velocity?

12 PRECALCULUS GTIH VECTOR WORKSHEET.Jf. "--.../. A ship steams 00 miles east, and then 40 miles on a heading of 20, How far is the ship and how does it bear from its starting point? 2. A ship sails 50 miles on a heading of 220 and then turns and sails directly east 'for 50 miles. How far is the ship and how does it bear from its starting point? 3. An airplane flies on a compass heading of 90 at 200 miles per hour. The wind affecting the plane is blowing from 300 at 30 miles per hour. What is the true course and ground speed of the airplane?. 4. Let the airplane in Exercise 3 fly 250 miles per hour on a heading of 80. lf the wind direction and speed are the same as given, what are the true course and ground speed of the airplane: 6, At what compass heading and air speed should an aircraft fly if a wind of 40 miles per hour is blowing from the north, and the pilot wants to maintain a ground speed of 200 miles per hour on a true course of 90? 6. Let the wind in Exercise 5 be blowing at 40 miles per hour from 305, while the pilot still maintains the same true course and ground speed. What should be his compass heading and air speed? 7. A ship is moving through the water on a compass heading of 30 c at a speed of 20 knots (nautical miles per hour). It is traveling in a current that causes the ship to move on a path with a heading of 45~. Find the speed of the current if it is flowing directly from the north. 8. A plane is flying with a compass heading of 300~ at an air speed of 300 miles per hour. If its true course is observed to be 330, and if the wind is blowing from 245, what is the speed of the wind? 9. Two ships leave a harbor, one traveling at 20 knots on a course of SOc and the other at 24 knots on a course of 40. How far apart are the ships after two hours? What is the bearing from the first' ship to the second at that time? 0. Two airplanes leave an airport at noon. one flying on a true course of 345= and the other on a true course of.f5~. If the first airplane averages 240 miles per hour ground speed and the other 200 miles per hour ground speed, how far apart are the airplanes after one hour? How does the second airplane bear from the first '). A pilot makes a flight plan that will take him from city A to city B, a distance of 400 miles. City B bears 60 from city A. and the wind at the planned flight altitude is 30 miles per hour from 60. If the airplane cruises at 320 miles per hour air speed, and if the pilot takes off at noon. what will be his compass heading and what is his ETA (estimated time of arrival) at city B? 2. When the pilot in Exercise decides to return to city A, the wind has shifted to 40 miles per hour from 90, What must be his compass heading for the return trip, and, if he takes off at 6 :00 P.M., what will be his ETA at city A7

13 Tuesday-Wednesday, March 6 and 7 Sample Problems for Test Review I. Look at the parallelogram below. Given: each of the following in terms of x and y. AB x AD y and P is the midpoint of AC and B P C BD, find A D. BC = 2. AB = 3. DC = 4. DB = 5. CB = 6. BP = 7. CA = 8. PA = 9. PC = II: In ABC, v and w. AP PB 2 PQ and. QC 3 A If PQ v and QB w, express the following in terms of P Q B C 0. BP =. PC = 2. BC = 3. AP = 4. PA = 5. BA = 6. AC = 7. AB =

14 III. The initial point and terminal point are given. Find the component form and the magnitude of the vector. initial point terminal point 8. (, ) (9,3) 9. (-3, -5) ( 5, ) 20. (-2, 7) (5,-7) 2. (-3, ) (5,6) 22. (0, -2) (3,6) 23. (-6, 4) (0,) IV. Find the resultant vector given u 3,9 v 4, 6 w 2, 24. u - v 25. u v u - 3v 27. 2u v w 2