area between two curves 27 videos

The Angle Between Vectors
Precalculus Vectors and Parametric Equations
How to compute the angle between two vectors.
dot product angle between vectors position vectors 
Area With the Cross Product
Precalculus Systems of Linear Equations and Matrices
How to show that the magnitude of the cross product of two vectors gives the area of the parallelogram determined by those two vectors.
cross product magnitude of vectors dot product angle between vectors area parallelogram 
Area With Determinants
Precalculus Systems of Linear Equations and Matrices
How to compute the area of a parallelogram using a determinant.
parallelogram vectors determinant area 
Using Sine to Calculate the Area of a Triangle
Precalculus Basic Trigonometry
How to calculate the area of any triangle using two sides and an included angle.
area of a triangle sine 
The Angle Between Planes
Precalculus Vectors and Parametric Equations
How to find the angle between planes, and how to determine if two planes are parallel or perpendicular.
normal vector the angle between planes perpendicular planes dot product scalar multiple parallel planes 
Families of Polar Curves: Roses
Precalculus Polar Coordinates and Complex Numbers
How to describe Roses, the family of curves with equations r=acos(b*theta) or r=asin(b*theta) when b >=2 and is an integer.
polar graph polar equation polar curve roses symmetric about the x axis symmetric about the y axis. 
The Resultant of Two Forces
Precalculus Vectors and Parametric Equations
How to find the resultant of two forces when they are parallel, opposite, or perpendicular in direction.
Forces Resultant Vector Addition Magnitude Direction The Pythagorean Theorem 
Families of Polar Curves: Conic Sections
Precalculus Polar Coordinates and Complex Numbers
How to describe the polar equations of conic sections.
polar graph polar equation polar curve conic sections focus origin pole parabola symmetric about the x axis parabola vertex 
Families of Polar Curves: Circles, Cardiods, and Limacon
Precalculus Polar Coordinates and Complex Numbers
How to graph the special cases of the family r = a + b cos (theta) when a or b = 0.
polar graph polar equation polar curve circles center radius completing the square 
Find an Equation for the Sine or Cosine Wave
Precalculus Trigonometric Functions
How to identify the graph of a stretched cosine curve.
sine cosine period amplitude intercepts turning points 
Graphing Polar Equations
Precalculus Polar Coordinates and Complex Numbers
How to sketch a simple polar curve by plotting points.
polar graph polar equation 
Parametric Equations and Motion
Precalculus Vectors and Parametric Equations
How to graph a parametric curve, and how to eliminate the parameter to obtain a rectangular equation for the curve.
position time parametric equations path rectangular equation eliminating the parameter square root function direction of motion 
Applied Linear Equations: Mixture Problem
Precalculus Linear Equations and Inequalities
How to solve a mixture problem when the size difference between the two containers is known.
word problem mixture 
Adding Vectors
Precalculus Vectors and Parametric Equations
How to add vectors geometrically two ways.
Displacement Vector Addition Head to Tail Method Parallelogram Method 
The Dot Product of Vectors
Precalculus Vectors and Parametric Equations
How to compute the dot product of two vectors.
vector components component form dot product scalar product 
Multiplying Complex Numbers
Precalculus Polar Coordinates and Complex Numbers
How to multiply two complex numbers in trigonometric form.
complex numbers trigonometric form modulus argument 
Dividing Complex Numbers
Precalculus Polar Coordinates and Complex Numbers
How to divide two complex numbers in trigonometric form.
complex numbers trigonometric form modulus argument conjugate 
The Inverse of a Square Matrix
Precalculus Systems of Linear Equations and Matrices
How to determine whether two matrices are inverses.
matrices square matrices the identity matrix matrix multiplication invertible inverse matrix 
The Cross Product of Vectors
Precalculus Systems of Linear Equations and Matrices
How to compute the cross product of two 3D vectors.
unit vectors components cross product determinant 
Cramer's Rule
Precalculus Systems of Linear Equations and Matrices
How to solve a system of two linear equations with two unknowns using Cramer's rule.
systems of linear equations Cramer's rule determinant coefficient matrix