Trigonometrical Ratios of Standard Angles

Using an equilateral triangle with side

Using an equilateral triangle with side 2a, when we draw a perpendicular from one vertex to the opposite side, we create two 30-60-90 triangles. From

Using a right

Using a right-angled isosceles triangle where both legs are equal (length a), the hypotenuse becomes a√2. This gives us: sin 45° = cos 45° = 1/√2, tan

The complete table shows all six

The complete table shows all six trigonometric ratios for angles 0°, 30°, 45°, 60°, and 90°. Students must memorize this table as it forms the basis f

When two angles add up

When two angles add up to 90°, their trigonometric ratios have special relationships: sin x° = cos(90° - x°), tan x° = cot(90° - x°), sec x° = cosec(9

Three key identities hold for any

Three key identities hold for any angle: sin²A + cos²A = 1, sec²A - tan²A = 1, and cosec²A - cot²A = 1. These can be verified using standard angles an