Preview Mode – Limited Content
This is a preview of the content. Only the first few sections are shown. Purchase the full content to access all content.

Trigonometric Identity & Graphs of Inverse Trigonometric Ratios; Pythagoras Theorem

Further Mathematics SS 2 Week WEEK .......... Preview
Lesson Details (Preview)

Week Range: ................... - ...................

Date: ...................

Time: ...................

Duration: 40 minutes minutes

Theme: Trigonometry and Geometry Applications

Sub-topic: Trigonometric Identities, Inverse Trig Graphs, and Pythagoras Theorem

Learning Objectives (Preview)

By the end of the lesson, students should be able to:

  1. Verify the fundamental trigonometric identity $\sin^2 \theta + \cos^2 \theta = 1$ using a right-angled triangle.
  2. Sketch the graphs of $y = \sin^{-1} x$, $y = \cos^{-1} x$, and $y = \tan^{-1} x$ stating their domains and ranges.
  3. +1 more objectives in full version
Rationale (Preview)
This lesson consolidates core trigonometric concepts required for WAEC and NECO Further Mathematics examinations. It bridges the gap between algebraic [Preview only]
Presentation Steps (Preview)
Step / Time Teacher's Activities Student's Activities Learning Points
Step 1: 5 minutes - Introduction & Review
Recap the definition of $\sin \theta$, $\cos \theta$, and $\tan \theta$ in a right-angled triangle. [Preview only]
Students recall previous knowledge and answer the inverse question verbally. They copy the Pythagore [Preview only]
Review of trigonometric ratios and introduction to the concept of inverse functions.
Step 2: 10 minutes - Deriving the Identity
Draw a right-angled triangle with sides $a$, $b$, and hypotenuse $c$. Show that $\sin \theta = \frac [Preview only]
Students follow the derivation on the board and replicate the steps in their notebooks, verifying th [Preview only]
Understanding that $\sin^2 \theta + \cos^2 \theta = 1$ is a direct consequence of the Pythagorean th [Preview only]
+2 more steps in full version
Student Note (Preview)
1,480 characters total — showing first 400
## Trigonometric Identities, Inverse Graphs & Pythagoras **What is this topic?** This lesson connects the Pythagorean theorem to trigonometry, showing that $\sin^2 \theta + \cos^2 \theta = 1$. It also covers how to draw the graphs of inverse trigonometric functions like $\sin^{-1} x$. **Key Points** 1. **Identity:** $\sin^2 \theta + \cos^2 \theta = 1$ for all angles $\theta$. 2. **Inverse Graphs:* [Preview only]

Full Content Locked

This is just a preview. Purchase the full content to access all content, including:

Buy Full Plan (₦500) Browse More