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Trigonometrical Ratios — Flashcards

ICSE · Class 9 · Mathematics

26 flashcards for Trigonometrical Ratios (ICSE Class 9 Mathematics) to test yourself on key terms and facts. Sample: "In a right-angled triangle ABC"

36 questions26 flashcards16 formulas & key relations5 concepts

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A right-angled triangle with one acute angle labeled as the angle of reference. The sides opposite to the acute angle, adjacent to the acute angle, and opposite to the right angle are clearly labeled
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26 Flashcards·
Pythagoras theorem in trigonometrySine ratioCosine ratioTangent ratioCosecant ratioSecant ratioFinding all ratios from one ratioExpression using sec and tan
Card 1Pythagoras theorem in trigonometry

In a right-angled triangle ABC, the hypotenuse AC = 13 cm and one leg AB = 5 cm. Find BC.

Answer

Step 1: Use Pythagoras theorem: AC^2 = AB^2 + BC^2. Step 2: Put the values: 13^2 = 5^2 + BC^2. Step 3: 169 = 25 + BC^2. Step 4: BC^2 = 144. Step 5: BC = 12 cm. Answer: BC = 12 cm.

Card 2Sine ratio

For angle A in triangle ABC, what is sin A when BC = 12 cm and AC = 13 cm?

Answer

Step 1: For angle A, sin A = perpendicular / hypotenuse. Step 2: Here, perpendicular = BC and hypotenuse = AC. Step 3: sin A = BC / AC = 12 / 13. Answer: sin A = 12/13.

Card 3Cosine ratio

For angle A in triangle ABC, find cos A when AB = 5 cm and AC = 13 cm.

Answer

Step 1: For angle A, cos A = base / hypotenuse. Step 2: Here, base = AB and hypotenuse = AC. Step 3: cos A = AB / AC = 5 / 13. Answer: cos A = 5/13.

Card 4Tangent ratio

For angle A in triangle ABC, find tan A when BC = 12 cm and AB = 5 cm.

Answer

Step 1: For angle A, tan A = perpendicular / base. Step 2: Here, perpendicular = BC and base = AB. Step 3: tan A = BC / AB = 12 / 5. Answer: tan A = 12/5.

Card 5Cosecant ratio

For angle A in triangle ABC, find cosec A when AC = 13 cm and BC = 12 cm.

Answer

Step 1: For angle A, cosec A = hypotenuse / perpendicular. Step 2: Here, hypotenuse = AC and perpendicular = BC. Step 3: cosec A = AC / BC = 13 / 12. Answer: cosec A = 13/12.

Card 6Secant ratio

For angle A in triangle ABC, find sec A when AC = 13 cm and AB = 5 cm.

Answer

Step 1: For angle A, sec A = hypotenuse / base. Step 2: Here, hypotenuse = AC and base = AB. Step 3: sec A = AC / AB = 13 / 5. Answer: sec A = 13/5.

Card 7Finding all ratios from one ratio

If cot A = 4/3 in a right-angled triangle, find all other trigonometrical ratios of angle A.

Answer

Step 1: cot A = base / perpendicular = 4 / 3. Step 2: Let base = 4x and perpendicular = 3x. Step 3: Hypotenuse^2 = (4x)^2 + (3x)^2 = 16x^2 + 9x^2 = 25x^2. Step 4: Hypotenuse = 5x. Step 5: sin A = 3x /…

Card 8Expression using sec and tan

If 13 sin A = 12, find sec A - tan A.

Answer

Step 1: 13 sin A = 12, so sin A = 12/13. Step 2: Let perpendicular = 12x and hypotenuse = 13x. Step 3: Use Pythagoras theorem: AB^2 + (12x)^2 = (13x)^2. Step 4: AB^2 = 169x^2 - 144x^2 = 25x^2. Step 5:…

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Frequently Asked Questions

What are the important topics in Trigonometrical Ratios for ICSE Class 9 Mathematics?
Key topics in Trigonometrical Ratios include Basic Ideas in a Right Triangle, Six Trigonometrical Ratios, Worked Calculations and Standard Results, Geometry-Based Applications. Study these first, then practise questions on each for Class 9 exams.
How many flashcards are available for Trigonometrical Ratios?
There are 26 flashcards for Trigonometrical Ratios covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Trigonometrical Ratios for Class 9 exams?
Learn the core ideas first, then work through the 36 practice questions on Trigonometrical Ratios. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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