A pre-Calculus journey of Trigonometry

Name: A pre-Calculus journey of Trigonometry
Rating: 4.3 (15 reviews)

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

Created byLearning 0to1

Last updated 1/2024

English

English [Auto],

What you'll 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

Course content

5 sections • 12 lectures • 58m total length

Introduction2:57
Explore how to construct the sine table using geometric derivations, Pythagorean theorem, and trig identities, deriving sines for 30, 45, 75, 15, 18, and 1 degree with algebra and Excel.

Meanings of sine1:52
Explore the meanings of sine and cosine through a circle projection forming a right triangle, with sine theta as opposite over hypotenuse and cosine as adjacent over hypotenuse.
How to get sines of some special angles: 30,45,60 degrees - Geometry3:41
Explore geometrical derivations of sines and cosines for 30, 45, and 60 degrees using Pythagoras theorem and complementary angles.
How to prove Pythagorean theorem1:33
Explore a geometrical proof of the pythagorean theorem by using squares on a and b and a square of side a plus b to show a^2 plus b^2 equals c^2.
How to derive the combination formula for trig4:22
Derive the sine and cosine addition formulas on a unit circle, using projections and similar triangles to express sin(a+b) and cos(a+b) in terms of sin and cos.

Section overview3:10
Explore how to derive sine and cosine values for special angles using the combination formula, bootstrapping, and signs to build a sine table.
How to find sine 15 - solving a quadratic equation6:42
Use a trick identity to relate sine 45 to sine 30 and sine 15, then solve a quadratic via completing the square to obtain sine 15 and cosine 15.
How to find sine 18 - quadratic formula6:35
Learn how to find sine 18 via a quadratic equation and completing the square, expressing sine and cosine through angles 18, 36, and 54 degrees.
How to evaluate sine 3 - Excel9:00
Learn how to evaluate sine of three degrees by using signs of 18 and 15, mirroring the 45-degree breakdown, and perform the calculation in Excel.

How to solve for sine1 - cubic equation4:07
Explore how the triple angle formula links sine three theta to sine theta, forming a cubic equation, and learn both analytical approaches and numerical methods to solve it.
How to solve for sine 1 - numerical methods using Excel10:15
Solve sine 1 degree with Excel numerical methods, cycling through trials using x0, h, and n to minimize the absolute value of the puzzle result and locate the best estimate.

Requirements

No requirement needed.

Description

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.

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.

Who this course is for:

Students who have trouble with trigonometry
Learners who are curious about how trigonometry was handled in the old days
People who want to learn math in a more meaningful way

A pre-Calculus journey of Trigonometry

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 3min

How to use geometry to obtain basic sines: sin30, sin454 lectures • 11min

How to use algebra to obtain special sines: sin15, sin18, sin34 lectures • 25min

How to use Excel and numerical methods to solve for sin12 lectures • 14min

Construct the sine table using Excel1 lecture • 4min

Requirements

Description

Who this course is for: