Trigonometry Formulas for Class 10 & 11 (Printable List)

Trigonometry starts in Class 10 with right-angled triangles and builds further in Class 11. This page collects the trigonometric ratios, the standard-angle values table and the core identities in one place, so you don't have to hunt through the textbook before an exam.

The Six Trigonometric Ratios

For an angle θ in a right-angled triangle, with the side opposite θ, the side adjacent to θ, and the hypotenuse:

Ratio	Definition
sin θ	Opposite / Hypotenuse
cos θ	Adjacent / Hypotenuse
tan θ	Opposite / Adjacent
cosec θ	Hypotenuse / Opposite (= 1 / sin θ)
sec θ	Hypotenuse / Adjacent (= 1 / cos θ)
cot θ	Adjacent / Opposite (= 1 / tan θ)

Memory trick — SOH-CAH-TOA: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent. The other three ratios (cosec, sec, cot) are just the reciprocals of sin, cos and tan.

Standard Angle Values (0°, 30°, 45°, 60°, 90°)

These exact values are asked directly in exams and are also needed to solve trigonometry problems quickly. Worth memorising properly rather than looking up every time.

Ratio	0°	30°	45°	60°	90°
sin	0	1/2	1/√2	√3/2	1
cos	1	√3/2	1/√2	1/2	0
tan	0	1/√3	1	√3	Not defined
cosec	Not defined	2	√2	2/√3	1
sec	1	2/√3	√2	2	Not defined
cot	Not defined	√3	1	1/√3	0

Quick way to rebuild this table in an exam: for sin, write 0, 1, 2, 3, 4 under 0°–90°, divide each by 4, then take the square root — you get 0, 1/2, 1/√2, √3/2, 1. For cos, just reverse the same row.

Reciprocal and Quotient Relationships

Relationship
sin θ = 1 / cosec θ
cos θ = 1 / sec θ
tan θ = 1 / cot θ = sin θ / cos θ
cot θ = cos θ / sin θ

The Three Core Trigonometric Identities

These hold true for every value of θ, and most trigonometry problems in Class 10 and 11 reduce to one of these three:

Identity	How it's derived
sin²θ + cos²θ = 1	From the Pythagorean theorem on a right triangle (the base identity)
1 + tan²θ = sec²θ	Divide sin²θ + cos²θ = 1 by cos²θ
1 + cot²θ = cosec²θ	Divide sin²θ + cos²θ = 1 by sin²θ

Worked example: if sin θ = 3/5, find cos θ and tan θ (θ acute).
Using sin²θ + cos²θ = 1: cos²θ = 1 − (3/5)² = 1 − 9/25 = 16/25, so cos θ = 4/5.
tan θ = sin θ / cos θ = (3/5) ÷ (4/5) = 3/4.

Frequently Asked Questions

What are the 6 trigonometric ratios?
sin, cos, tan, cosec, sec and cot — defined as ratios of the sides of a right-angled triangle relative to one of its acute angles.

Why is tan 90° not defined?
Because tan θ = sin θ / cos θ, and cos 90° = 0. Dividing by zero is not defined, so tan 90° (and sec 90°) have no value.

What is the easiest way to remember the standard angle table?
For sin, write 0,1,2,3,4 in a row, divide each by 4 and take the square root. Reverse that row to get cos. tan is then sin divided by cos for each angle.