Trigonometric ratios
Trigonometric ratios are the fixed ratios between the sides of a right triangle for a chosen acute angle.
Practice This ConceptMain explanation
Teacher explanation
For one acute angle in a right triangle, the sides keep a fixed proportion. That is why ratios like sine, cosine, and tangent depend on the angle, not on the size of the triangle. If two right triangles have the same acute angle, the ratios for that angle stay the same.
Example
If two right triangles both have angle A equal to 30 degrees, then the ratio opposite side divided by hypotenuse for angle A will be the same in both triangles.
Simple analogy
Think: opposite is across, adjacent is beside, hypotenuse is the longest side.
Common confusion
Students often mix up opposite side and adjacent side, especially when the triangle is drawn in a different orientation.
Exam tip
Always identify the chosen angle first, then label opposite, adjacent, and hypotenuse before writing any ratio.
Study the trigonometric ratios diagram carefully
Use the labelled diagram to keep trigonometric ratios clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of trigonometric ratios in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on trigonometric ratios.
Revision cue
Revise trigonometric ratios through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of trigonometric ratios in one clean line.
2-mark use
Define trigonometric ratios and add one example or condition.
3-mark use
Explain trigonometric ratios, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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