Trigonometric ratios
- CBSE · NCERT Class 10, Ch 8 Introduction to Trigonometry
A trigonometric ratio compares two sides of a right triangle, seen from one of its sharp angles, such as sin A, cos A or tan A.
Take a right triangle and pick one of its two sharp angles. Call it angle A. The longest side is the hypotenuse. The side facing angle A is the opposite side. The other short side touches angle A and is the adjacent side. A trigonometric ratio divides one side by another.
- sin A = opposite side ÷ hypotenuse.
- cos A = adjacent side ÷ hypotenuse.
- tan A = opposite side ÷ adjacent side.
- cosec A, sec A and cot A turn these upside down. They are 1 ÷ sin A, 1 ÷ cos A and 1 ÷ tan A.
A small example
A right triangle has sides 6 cm, 8 cm and 10 cm. The 10 cm side is the hypotenuse. Say the 6 cm side faces angle A. Then sin A = 6/10 = 3/5, cos A = 8/10 = 4/5 and tan A = 6/8 = 3/4. The ratios stay the same if the triangle is drawn bigger or smaller.
Where marks go
Question 29 of CBSE's 2026-27 Maths Basic sample paper gives two sides of a right triangle. It asks for two expressions in the ratios. In the 2026-27 Maths Basic marking scheme, the third side, found with Pythagoras, earns half a mark. Writing sin and cos from it earns another half. Each of the two answers then carries 1 mark.
So a slip in the last line still leaves the marks for the steps before it. That is step marking, and it works only when the steps are written down.
Sources
Facts last checked against these sources on 30 September 2026.
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