Trigonometrical Ratios of Standard Angles

In an equilateral triangle with side

In an equilateral triangle with side 2a, a perpendicular from one vertex divides the triangle into two right triangles. This gives BD = a and AD = √3·

In a right

In a right-angled isosceles triangle with AB = BC = a and ∠B = 90°, the hypotenuse AC = √2·a. Therefore sin 45° = 1/√2, cos 45° = 1/√2, and tan 45° =

The important values are sin 0°

The important values are sin 0° = 0, cos 0° = 1, sin 90° = 1, cos 90° = 0. The complete standard-angle values also give tan 90° and sec 90° as not def

As the angle increases from 0°

As the angle increases from 0° to 90°, sin increases from 0 to 1, cos decreases from 1 to 0, and tan increases from 0 to infinity.

For any angle

For any angle A, sin²A + cos²A = 1, sec²A - tan²A = 1, and cosec²A - cot²A = 1. Also, for every value of angle θ, 1 + tan²θ = sec²θ.