Chapter 7 Trigonometry

Ch 7  Applications of Trigonometry and Vectors

Ch 7.1  Oblique Triangles and the Law of Sines :

The Law of Sines: The Basics :
Solving the Triangle with A=48°, B=54°, a=12.5ft
http://www.youtube.com/watch?v=dxYVBbSXYkA

Solving the Triangle with C=102°, b=5m, c=18m
http://www.youtube.com/watch?v=LzdDALbFlxY

Finding the Distance Across the Canyon

http://www.youtube.com/watch?v=VqapJYCG31k

Finding the Distance of the Campsite from the Base of the Mountain and the Time Needed to the Base
http://www.youtube.com/watch?v=az3JAqNMGt4

Determining the Length of X
http://www.youtube.com/watch?v=9l23gPNAs_g

Determining the Distance from the Tower to the Airplane
Determining the Elevation of the Airplane
http://www.youtube.com/watch?v=6dEvIdTJ708

Determining the Area of a Triangle with A=35°, a=6cm, a=15cm
Determining the Area of a Triangle with B=72°, a=23.7 ft, b=25.2 ft
http://www.youtube.com/watch?v=mBFDq4bPXMs

Ch 7.2  The Ambiguous Case of the Law of Sines

Solving the Triangle with C=82°, a=11m, c=7m;
Solving the Triangle with A=88°, a=110ft, c=54ft;
Solving the Triangle with B=40°, b=22cm, a=30cm
http://www.youtube.com/watch?v=ETqe-_plC3Y

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with One solution given a=76, c=52, A=39° http://www.youtube.com/watch?v=CXU-zGTfHGM&feature=plcp

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with Two solutions given a=52, b=63, A=42°  http://www.youtube.com/watch?v=sXn_rkJE3WI&feature=plcp

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with No solutions given a=48, c=68, A=86° http://www.youtube.com/watch?v=u8zLE0buKPY&eature=plcp

Ch 7.3  The Law of Cosines

Solving Triangle ABC with B= 73.1°, a= 24.2 ft, c= 43.7 ft
Solving Triangle ABC with a= 25.4cm, a=42.8cm, c=59.3cm
http://www.youtube.com/watch?v=hBzKRHH_grk

Determining the Diagonal of a Parallelogram
http://www.youtube.com/watch?v=_NyWGW6Pu1w

Determining the Length of the Tunnel and the Bid Amount after 20% profit off the Cost
Determining the Duration of Service a Person gets when She is Driving Past a Transmission Tower at a Certain Speed
http://www.youtube.com/watch?v=1SvHQNBGU6Q

Determining the Flying Distance of A plane From Her Starting Position
http://www.youtube.com/watch?v=wu29Zdk_PZA

The Law of Cosines: Applications – Determining the Largest Angle of the Three Sides
http://www.youtube.com/watch?v=-U97mrpL_aE

Determining the Areas of Triangles Using Heron’s Area Formula
http://www.youtube.com/watch?v=Pi56pFy-8HU

Ch 7.4  Vectors, Operations, and the Dot Product

Introduction to Vectors :
http://www.youtube.com/watch?v=IKzR0Odurm0

Vector Basics – Drawing Vectors/ Vector Addition
http://www.youtube.com/watch?feature=player_embedded&v=pimr9I92GZY

Finding x and y Components of a Vector with a Magnitude of 8 and at an Angle of 60° from the Origin
http://www.youtube.com/watch?feature=player_embedded&v=-fbCI2qcgRk

Finding x and y Components of Vectors
http://www.youtube.com/watch?v=R9f1t-OP358&feature=player_embedded

Drawing the Vector v=<2,3>;
Drawing the Vector   v=<–3,4>;
Finding the Vector  AB of (2, 1) and (5, 6)
http://www.youtube.com/watch?v=odhAVmAahb4&feature=player_embedded

Adding v+u and v+u+w  where v=<2, 2>, u=<3, 0> and w=<0, –6>;
Multiplying 10u  where u=<1, 4>;
Simplifying u–2w  where  u=<1,4> and w=<–2, 3>
http://www.youtube.com/watch?feature=player_embedded&v=IUzoNG4-MIc

Finding the Magnitude and Direction of Vector <–3, 4>
http://www.youtube.com/watch?v=WxWJorOVIj8&feature=player_embedded

Finding the Magnitude and Direction of Vector <–2, –5>
http://www.youtube.com/watch?v=-gokuNjpyNg&feature=player_embedded

Finding the Magnitude and Direction of Vector <2, 6> and <3, –10>
http://www.youtube.com/watch?v=ZDMm8mtDWhE&feature=player_embedded

Finding Dot Products a·b  where a=<2, 5> and b=<–3, 1>;
Finding the Angle of a=6i–2j–3k and b=i+j+k;
Determining if a=<2, 4> and b=<4, –2> are Orthogonal
http://www.youtube.com/watch?v=98C7iv8OcnI&feature=player_embedded

Finding Dot Product u·v  and u(v+w) Givern v=<-1, 5> andw=<–3, 1>;
Angle Between Two Vectors;

Parallel and Orthogonal Vectors;

Finding the Angle Between u=<-2, 3> and v=<1, -5>;
Determining if Two Vectors u=<-4, 2> and v=<1, 2> are Orthogonal;

Definition of the Component of Vector a along Vector b; http://www.youtube.com/watch?v=c5mSscgulIXg&list=PL554F9F460401DF50&index=38&feature=plpp_video

 

Ch 7.5  Applications of Vectors

Finding the Distance between the Ship and the Port and its Bearing
Finding the Direction and Magnitude of the Resultant Force of Two Trucking Pulling on a Truck Stuck in the Mud
http://www.youtube.com/watch?v=53UdTRt_re0

Definition of Work Done;
Finding the Force required to Keep the Piano from Rolling Down the Ramp;
Finding the Work Done needed for a Man to Push the Broom for a Distance http://www.youtube.com/watch?v=c5mSscgulXg&list=PL554F9F460401DF50&index=38&feature=plpp_video (The Last Three Parts of the Video)

Finding the Magnitude and Direction of the Resulting Force of Two Forces Acting on an Airplane http://www.youtube.com/watch?v=X5xPr2WIboM&feature=plcp

Finding the work needed to Push a Vehicle to the Gas Station http://www.youtube.com/watch?v=UhKg-jSgsjk&feature=plcp