See how elementary math skills are used to construct a sine table!

What you will learn

Geometry: Pythagorean theorem, Trig identity

Algebra: Solving quadratic equations, complete the square, quadratic formulas

Using Numerical methods to solve Cubic equation

Solving for sine1 using Excel

Construct the sine table using Excel


Trigonometry played important roles in navigation, science and engineering. Modern days we have computing devices spitting out results easily, but how did mathematicians in the old times tackle this problem? Walking through the various methods employed to construct a sine table is the central topic of this course.

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We’ve studied lots of math tools in school, such as algebra, geometry, quadratic equations, quadratic formulas, you might can’t help but wondering: where on earth did they come from and what’s the use of them anyway? Math is a complex toolbox with different toolsets meant to help us tackle real life problems. Like learning any other tools in life, the best way to learn them is through different projects. This mini-course on trigonometry will do that! Through exploring the knowledge of trigonometry in the middle ages, you will encounter different elementary math skills like geometric reasoning, Pythagorean Theorem, Trig identities, solving quadratic equations, emergence of a cubic equations, and using numerical methods to solve a cubic equation. Unlike traditional school where subjects are taught in an isolated manner, in this course these different topics are orchestrated toward a central theme to construct a sine table. The knowledge revealed will also provide you the basis towards our modern approach in handling trigonometry.





How to use geometry to obtain basic sines: sin30, sin45

Meanings of sine
How to get sines of some special angles: 30,45,60 degrees – Geometry
How to prove Pythagorean theorem
How to derive the combination formula for trig

How to use algebra to obtain special sines: sin15, sin18, sin3

Section overview
How to find sine 15 – solving a quadratic equation
How to find sine 18 – quadratic formula
How to evaluate sine 3 – Excel

How to use Excel and numerical methods to solve for sin1

How to solve for sine1 – cubic equation
How to solve for sine 1 – numerical methods using Excel

Construct the sine table using Excel

How to construct sine table using Excel