Trigonometrical Ratios
ICSE · Class 9 · Mathematics
Flashcards for Trigonometrical Ratios — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allIn 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.
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.
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.
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.
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.
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.
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 /…
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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