Alternate coordinate systems (bases) (Khan Academy)

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We explore creating and moving between various coordinate systems. (1) Orthogonal complements Orthogonal complements dim(v) + dim(orthogonal complement of v) = n Representing vectors in rn using subspace members Orthogonal complement of the orthogonal complement Orthogonal complement of the nullspace Unique rowspace solution to Ax = b Rowspace solution to Ax = b example (2) […]

Vectors and spaces (Khan Academy)

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Let’s get our feet wet by thinking in terms of vectors and spaces. (1) Vectors Vector intro for linear algebra Real coordinate spaces Adding vectors algebraically & graphically Multiplying a vector by a scalar Vector examples Scalar multiplication Unit vector notation Unit vectors Add & subtract vectors Add vectors: magnitude & direction to component Parametric […]

Derivative applications (Khan Academy)

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The reason we study calculus, and the reason it was invented, is for its many uses in real-world problems. In particular, derivatives let us optimize functions and study their rates of change. Here we cover optimization, rates of change, L’Hopital’s rule, the mean value theorem, and more! (1) Equations of normal and tangent lines Equation […]

Trigonometric equations and identities (Khan Academy)

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Learn how to solve trigonometric equations and how to use trigonometric identities to solve various problems. (1) Trig identity reference Trig identity reference (2) The inverse trigonometric functions Intro to arcsine Intro to arctangent Intro to arccosine Evaluate inverse trig functions Restricting domains of functions to make them invertible Domain & range of inverse tangent […]

Graphs of trigonometric functions (Khan Academy)

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Learn how to graph trigonometric functions and how to interpret those graphs. Learn how to construct trigonometric functions from their graphs or other features. (1) The graphs of sine, cosine, and tangent Graph of y=sin(x) Graph of y=tan(x) Intersection points of y=sin(x) and y=cos(x) (2) Introduction to amplitude, midline, and extrema of sinusoidal functions Features […]

Trigonometry with right triangles (Khan Academy)

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Learn the basics of trigonometry: What are sine, cosine, and tangent? How can we use them to solve for unknown sides and angles in right triangles? (1) Introduction to the trigonometric ratios Sides of right triangles Intro to the trigonometric ratios Trigonometric ratios in right triangles Trigonometric ratios in right triangles Trigonometric ratios in right […]

Geometric constructions (Khan Academy)

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We now have fancy computers to help us perfectly draw things, but have you ever wondered how people drew perfect circles or angle bisectors or perpendicular bisectors back in the day. Well this tutorial will have you doing just as your grandparents did (actually, a little different since you’ll still be using a computer to […]

Perimeter, area, and volume (Khan Academy)

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A broad set of tutorials covering perimeter area and volume with and without algebra. (1) Basic area Perimeter & area Area of triangles intuition Area of triangles Area of triangles Area of parallelograms intuition Area of parallelograms Area of trapezoids Area of trapezoids Area of kites (2) Advanced perimeter and area Area of a triangle […]

Circles (Khan Academy)

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Explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents. (1) Circle basics Circles glossary Radius, diameter, circumference & π Proof: all circles are similar (2) Arc measure Intro to arc measure Finding arc measures Arc measure Finding arc measures with equations Arc […]

Right triangles and trigonometry (Khan Academy)

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Triangles are not always right (although they are never wrong), but when they are it opens up an exciting world of possibilities. Not only are right triangles cool in their own right (pun intended), they are the basis of very important ideas in analytic geometry (the distance between two points in space) and trigonometry. (1) […]