Trigonometric Ratios for Standard Angles — Full Chart & Quick Revision
Essential trigonometric ratios (sin, cos, tan) for standard angles 0, 30, 45, 60, and 90 degrees. Critical for trigonometry, geometry, and physics problems
TL;DR: Essential trigonometric ratios (sin, cos, tan) for standard angles 0, 30, 45, 60, and 90 degrees. Critical for trigonometry, geometry, and physics pro…
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Essential trigonometric ratios (sin, cos, tan) for standard angles 0, 30, 45, 60, and 90 degrees. Critical for trigonometry, geometry, and physics problems
Trigonometric Ratios for Standard Angles — Full Chart
| Item | Value |
|---|---|
| sin(0 degrees) | 0 |
| sin(30 degrees) | 1/2 |
| sin(45 degrees) | sqrt(2)/2 or 1/sqrt(2) |
| sin(60 degrees) | sqrt(3)/2 |
| sin(90 degrees) | 1 |
| cos(0 degrees) | 1 |
| cos(30 degrees) | sqrt(3)/2 |
| cos(45 degrees) | sqrt(2)/2 or 1/sqrt(2) |
| cos(60 degrees) | 1/2 |
| cos(90 degrees) | 0 |
| tan(0 degrees) | 0 |
| tan(30 degrees) | 1/sqrt(3) or sqrt(3)/3 |
| tan(45 degrees) | 1 |
| tan(60 degrees) | sqrt(3) |
| tan(90 degrees) | undefined or infinity |
| cot(30 degrees) | sqrt(3) |
| cot(45 degrees) | 1 |
| cot(60 degrees) | 1/sqrt(3) |
| sec(0 degrees) | 1 |
| cosec(90 degrees) | 1 |
FAQs
How do I remember the sine and cosine values for standard angles?
Use the pattern: sin(0, 30, 45, 60, 90) = 0, 1/2, sqrt(2)/2, sqrt(3)/2, 1. For cosine, reverse the order: 1, sqrt(3)/2, sqrt(2)/2, 1/2, 0.
What does it mean that tan(90 degrees) is undefined?
tan(90 degrees) = sin(90)/cos(90) = 1/0, which is undefined. Geometrically, the tangent line is vertical and has no finite slope at 90 degrees.