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Precalculus » F. Polar Coordinates and Vectors

  • F.1. Polar Coordinates

    1. F.1.M. Play Multiplayer 0 wins, 0 losses

    2. F.1.Q. Unit Challenge

    3. F.1.1. Polar Coordinates

      1. F.1.1.O. Overview
      2. F.1.1.1. Plot the point in the polar coordinate system
      3. F.1.1.2. Find another polar representation of the given point
      4. F.1.1.3. Convert the polar coordinate to a rectangular coordinate
      5. F.1.1.4. Convert the rectangular coordinate to a polar coordinate

    4. F.1.2. Polar Equations

      1. F.1.2.O. Overview
      2. F.1.2.1. Convert an equation in rectangular form to a polar equation
      3. F.1.2.2. Convert a polar equation to rectangular form

    5. F.1.3. Graphing Polar Equations

      1. F.1.3.O. Overview
      2. F.1.3.1. Test for symmetry with respect to θ = π / 2, the polar axis, and the pole
      3. F.1.3.2. Find the maximum value of |r| and any zeros of r
      4. F.1.3.3. Sketch the graph of a polar equation
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  • F.2. Vectors in the Plane

    1. F.2.M. Play Multiplayer 0 wins, 0 losses

    2. F.2.Q. Unit Challenge

    3. F.2.1. Vectors and Component Form

      1. F.2.1.O. Overview
      2. F.2.1.1. Show that two vectors in a plane are equivalent
      3. F.2.1.2. Find the component form and magnitude of the vector given a graph
      4. F.2.1.3. Find the component form and magnitude of the vector given an initial point and terminal point
      5. F.2.1.4. Graph the vector using vector operations
      6. F.2.1.5. Find the resultant vector given two vectors in component form

    4. F.2.2. Unit Vectors

      1. F.2.2.O. Overview
      2. F.2.2.1. Find the unit vector in the direction of the given vector
      3. F.2.2.2. Find the vector with the given magnitude and direction
      4. F.2.2.3. Write a linear combination of the standard unit vectors given the initial point and terminal point
      5. F.2.2.4. Find the component form of the vector given an equation relating two vectors

    5. F.2.3. Direction Angles

      1. F.2.3.O. Overview
      2. F.2.3.1. Find the magnitude and direction angle of the vector
      3. F.2.3.2. Find the component form of the vector given its magnitude and the angle it makes with the positive x-axis
      4. F.2.3.3. Find the component form of the sum of two vectors with the given direction angles
      5. F.2.3.4. Use the Law of Cosines to find the angle between two vectors
      6. F.2.3.5. Word Problems – use vectors to find speed and direction
      7. F.2.3.6. Word Problems – resultant force
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  • F.3. Vectors and Dot Products

    1. F.3.M. Play Multiplayer 0 wins, 0 losses

    2. F.3.Q. Unit Challenge

    3. F.3.1. Dot Product of Two Vectors

      1. F.3.1.O. Overview
      2. F.3.1.1. Find the dot product of the two vectors
      3. F.3.1.2. Perform the vector operation and state whether the result is a vector or a scalar
      4. F.3.1.3. Use the dot product to find the magnitude

    4. F.3.2. The Angle Between Two Vectors

      1. F.3.2.O. Overview
      2. F.3.2.1. Find the angle between two vectors
      3. F.3.2.2. Determine whether the two vectors are orthogonal, parallel, or neither

    5. F.3.3. Finding Vector Components

      1. F.3.3.O. Overview
      2. F.3.3.1. Find the projection of the vector and then write the vector as the sum of two orthogonal vectors
      3. F.3.3.2. Word Problems – Finding a Force
      4. F.3.3.3. Word Problems – Finding Work
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