Understanding Trigonometric Ratios and Exact Values

This comprehensive page introduces the fundamental concepts of trigonometric ratios sin cos tan explained and their exact values for common angles.

Definition: The three main trigonometric ratios are defined as:

• Sine = Opposite/Hypotenuse
• Cosine = Adjacent/Hypotenuse
• Tangent = Opposite/Adjacent

Highlight: Key angles to remember are 0°, 30°, 45°, 60°, and 90°, each with specific exact values.

Example: For 30°:

• sin 30° = 1/2
• cos 30° = √3/2
• tan 30° = 1/√3

Vocabulary:

• Opposite: The side opposite to the angle in question
• Adjacent: The side next to the angle in question
• Hypotenuse: The longest side of a right-angled triangle, opposite to the right angle

The page includes a practical example demonstrating steps for solving trigonometry problems: "Work out one possible value of 'y' given: 4 × sin 30° × tan 30° × cos 30° = sin y"

Highlight: When calculating angles using trigonometric identities, it's crucial to remember that some ratios are undefined at certain angles, such as tan 90°.