Скачать или смотреть Calculus Foundations: The Ultimate Trigonometry Refresher

Unlock the geometric foundations of Calculus. Success in high-level mathematics is built on a mastery of spatial reasoning and trigonometric identities.

🎓 ACCESS ALL 15 INDIVIDUAL LESSONS AND PDF GUIDES ON MY WEBSITE: https://www.mathsadviceonyourdevice.c...

This 30-minute masterclass is designed for Calculus teachers seeking high-quality classroom resources and students needing a comprehensive prerequisite refresher before diving into limits and derivatives.

► WHY THIS REFRESHER IS ESSENTIAL:

🔹 VISUAL CONCEPTUALIZATION: We move beyond formulas to show WHY the Pythagorean Theorem works using area-based visualizations.

🔹 BRIDGING TO CALCULUS: Transition from static triangles to dynamic change by connecting linear gradients to the Tangent function: laying the groundwork for the derivative.

🔹 SPATIAL MASTERY: Master 2D and 3D distance formulas, essential for optimization problems and multivariable concepts.

🔹 EXACT PRECISION: Learn to work with surds and exact values: a non-negotiable skill for high-level Calculus exams.

🔹 REAL-WORLD MODELING: From navigation bearings to 3D pyramid volumes, we apply SOH-CAH-TOA to complex, multi-step problems.

► WHAT YOU WILL LEARN:

🔹 GEOMETRIC PROOFS: Visualizing area sums and solving for in-circle radii in "simplest triplets."

🔹 3D APPLICATIONS: Calculating the height, volume, and surface area of pyramids using Pythagoras in reverse.

🔹 ADVANCED TRIGONOMETRY: Mastery of the Sine Rule, Cosine Rule, and the Area of a Triangle formula.

🔹 COORDINATE GEOMETRY: How to find angles between intersecting lines using inverse tangents of gradients.

🔹 PROBLEM-SOLVING TACTICS: Breaking down "Double-Triangle" problems (Flagpoles, Summits, and Trees) using simultaneous equations.

🔹Video Chapters🔹
UNIT 1: COORDINATE & 3D GEOMETRY
0:00 – Introduction to Pythagoras Theorem
0:56 – Pythagorean Triplets & Calculation Shortcuts
1:51 – Distance Between Coordinates Formula
3:19 – Distance Formula in 3D Space
4:12 – Volume of a Square-Based Pyramid
5:15 – Surface Area of a Square-Based Pyramid
5:47 – TEACHER RESOURCE: Get the 15 PDF Practice Guides
UNIT 2: RIGHT-ANGLED TRIGONOMETRY
6:02 – Trigonometric Ratios: SOH CAH TOA Explained
6:52 – Calculating Missing Lengths in Right Triangles
8:44 – Calculating Missing Angles
9:49 – Angles of Elevation & Real-World Applications
13:32 – Finding the Angle Between a Line and a Plane
15:38 – The Angle Between y=mx+c and the x-axis
17:08 – Finding the Acute Angle Between Straight Lines
18:01 – Writing Trig Ratios in Exact Surd Form
UNIT 3: ADVANCED TRIANGLES & NAVIGATION
19:11 – The Sine Rule for Non-Right Triangles
22:14 – The Cosine Rule for Non-Right Triangles
24:35 – Area of a Triangle (1/2 ab sin C Method)
27:28 – Finding the Area of a Quadrilateral
28:18 – Bearings & Navigation in Real-Life Scenarios

I have designed this workshop to be modular so you can pick and choose the topics your students need most.

👉 GET THE 15 LESSONS & PDF GUIDES HERE: https://www.mathsadviceonyourdevice.com/

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