Trigonometry Ratios in 5 Minutes — Free Quick Revision
Learn Trigonometry Ratios in about 5 minutes — a free bite-sized module with a clear explanation, a worked example and a quick quiz for Indian students.
TL;DR: Learn Trigonometry Ratios in about 5 minutes — a free bite-sized module with a clear explanation, a worked example and a quick quiz for Indian student…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. Remember SOHCAHTOA.
Maths · Class 10 · about 7 minutes
The Idea
In a right triangle, the three main trigonometric ratios relate the angles to the sides.
SOHCAHTOA is the mnemonic: - Sin = Opposite / Hypotenuse - Cos = Adjacent / Hypotenuse - Tan = Opposite / Adjacent
In a right triangle, the "opposite" side is across from the angle you're measuring. The "adjacent" side is next to the angle. The hypotenuse is the longest side, opposite the right angle.
These ratios are *always the same* for a given angle, no matter how big or small the triangle. This is why trig tables and calculators work—sin(30°) is always 0.5.
Tangent also equals sin/cos: tan(θ) = sin(θ) / cos(θ).
Worked Example: Find a Side in a Right Triangle
Problem. In a right triangle, the angle is 35° and the hypotenuse is 10 cm. Find the opposite side.
Solution.
We know the hypotenuse and want the opposite side. Use sine:
sin(35°) = opposite / hypotenuse sin(35°) = opposite / 10 opposite = 10 × sin(35°) opposite ≈ 10 × 0.574 opposite ≈ 5.74 cm
Quick Quiz
Answer each one before reading the explanation beneath it.
1. In a right triangle, if cos(θ) = 3/5, what is sin(θ) if the opposite side is 4?
- 3/5
- 4/5 — correct
- 5/4
- 3/4
4/5
2. What is tan(θ) if sin(θ) = 0.6 and cos(θ) = 0.8?
- 0.75 — correct
- 0.6
- 0.8
- 1.33
0.75
3. In right triangle ABC with right angle at C, angle A = 40° and side BC (opposite to A) = 5. Find the hypotenuse AB.
- 5 / sin(40°) ≈ 7.78 — correct
- 5 × sin(40°) ≈ 3.21
- 5 × tan(40°) ≈ 4.19
- 5 / cos(40°) ≈ 6.53
5 / sin(40°) ≈ 7.78
All 5-minute modules → · Full chapter notes → · Chapter-wise MCQs →