International System and Trigonometric Ratios

This section covers the conversion between degrees and radians, as well as the basic trigonometric ratios.

Key topics:

• Converting between degrees and radians
• Defining sine, cosine, tangent and their reciprocals
• Trigonometric ratios in different quadrants

Vocabulary:

• Radian - The angle subtended at the center of a circle by an arc equal in length to the radius
• Cosecant (cosec) - The reciprocal of sine
• Secant (sec) - The reciprocal of cosine
• Cotangent (cotg) - The reciprocal of tangent

Highlight: The conversion factor between degrees and radians is π/180°.

The page also includes a diagram showing how trigonometric ratios relate to the sides of a right triangle in each quadrant.

Fundamental Trigonometric Relationships

This section presents the core trigonometric identities and demonstrates their proofs.

Key relationships covered:

1. sin^2 x + cos^2 x = 1
2. tan x = sin x / cos x
3. 1 + tan^2 x = 1 / cos^2 x

Definition: Trigonometric identity - An equation involving trigonometric functions that is true for all values of the variables.

Example: Proof of sin^2 x + cos^2 x = 1 using the Pythagorean theorem in a right triangle.

The page also includes a table of trigonometric ratios for common angles (0°, 30°, 45°, 60°, 90°), which is essential for solving many trigonometry problems.

Trigonometry Fundamentals and Problem Solving

This section introduces core trigonometric concepts and problem-solving techniques for angles in different quadrants.

Key topics covered:

• Calculating sine and cosine values given other trigonometric ratios
• Solving for unknown sides and angles in right triangles
• Using trigonometric identities

Example: For an angle in the first quadrant with cosine 3/4, the sine is calculated as √(1 - cos^2) = √(1 - (3/4)^2) = √(7/16) = √7/4.

Highlight: The fundamental trigonometric identity sin^2 x + cos^2 x = 1 is used frequently to solve problems.

Vocabulary: Tangent (tg) - The ratio of sine to cosine for an angle