Page 2: Trigonometric Ratios

The second page explores basic trigonometric ratios and their applications in right triangles, introducing sine, cosine, and tangent relationships.

Vocabulary:

• Sine (sin θ) = opposite/hypotenuse
• Cosine (cos θ) = adjacent/hypotenuse
• Tangent (tan θ) = opposite/adjacent

Example: In a right triangle with sides 3, 4, and 5 units, sin C = 3/5, cos C = 4/5, and tan C = 3/4.

Page 3: Introduction to Vectors

This page introduces vector concepts and their fundamental properties in physics, including definition and representation methods.

Definition: A vector is a quantity that has both magnitude and direction.

Highlight: Vector components can be broken down into x and y components parallel to the coordinate axes.

Example: Angles can be measured either counterclockwise from the positive x-axis or as degrees above/below the x-axis.

Page 4: Vector Components

Detailed explanation of vector component calculations using trigonometric functions, with practical applications.

Example: A plane flying at 123 km/h at 40° above the x-axis has components:

• X-component = 123 cos(40°) = 94.2 km/h
• Y-component = 123 sin(40°) = 79.1 km/h

Highlight: Component calculations rely on cosine for x-components and sine for y-components.

Page 5: Vector Component Practice

This page provides practice problems for calculating vector components with negative angles and forces.

Example: For 18 km at 47° below the positive x-axis:

• X-component = 18 cos(47°) = 12.3 km
• Y-component = 18 sin(47°) = -13.1 km

Page 6: Vector Addition

Introduction to vector addition methods and resultant vector calculations.

Definition: The resultant vector is the single vector that has the same effect as two or more vectors acting together.

Example: Adding 20 N East and 7 N North vectors results in a 21.2 N resultant at 19.3° above the positive x-axis.

Page 7: Advanced Vector Addition

Comprehensive coverage of vector addition problem-solving methodology with multiple examples.

Highlight: Four key steps for vector addition:

1. Sketch and resolve each vector
2. Add x and y components
3. Draw resultant triangle
4. Calculate magnitude and direction

Example: Adding vectors of 4.0m 90° below x-axis and 8.3m 55° above negative x-axis results in 5.6m at 30.3° above negative x-axis.

Page 7: Vector Addition Methods

This page outlines the systematic approach to vector addition problems.

Definition: Four key steps for solving vector addition problems are presented:

1. Sketch and resolve vectors
2. Add x and y components
3. Draw component triangle
4. Calculate resultant magnitude and direction

Example: Addition of vectors including 20 N along positive x-axis and another at 30° above.

Page 1: Pythagorean Theorem Review

This page introduces the fundamental relationship between sides of a right triangle using the Pythagorean theorem. The content focuses on practical problem-solving using the formula a² + b² = c².

Definition: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

Example: A right triangle with sides 8 and 6 units has its hypotenuse calculated as √$64 + 36$ = 10 units.

Highlight: The formula a² + b² = c² is essential for solving unknown sides in right triangles.