Trigonometry — Flashcards
Tamil Nadu Board · Class 9 · Mathematics
30 flashcards for Trigonometry (Tamil Nadu Board Class 9 Mathematics) to test yourself on key terms and facts.
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In a right-angled triangle ABC with right angle at B, if angle C = θ, AC = 13 cm (hypotenuse), and BC = 5 cm (adjacent to θ). Find sin θ.
Answer
Step 1: Identify the sides relative to angle θ. AC = hypotenuse = 13 cm, BC = adjacent = 5 cm. Step 2: Find the opposite side using Pythagoras theorem: AB² + BC² = AC² → AB² + 5² = 13² → AB² + 25 = 16…
Find all six trigonometric ratios for angle θ if tan θ = 3/4.
Answer
Step 1: From tan θ = 3/4, we know opposite/adjacent = 3/4. Let opposite = 3k and adjacent = 4k. Step 2: Find hypotenuse using Pythagoras: hypotenuse = √(3k)² + (4k)² = √(9k² + 16k²) = √(25k²) = 5k. St…
When do you use sin θ = opposite/hypotenuse? Give a practical example.
Answer
Use sin θ when you know (or need to find) the angle and the opposite side relative to that angle in a right-angled triangle, and you're given the hypotenuse or need to find it. EXAMPLE: A ladder of le…
Formula for: sin θ
Answer
sin θ = opposite side / hypotenuse Where: • opposite side = the side opposite to angle θ in a right-angled triangle • hypotenuse = the longest side of the right-angled triangle (opposite the right an…
In a right triangle, if sin A = 7/25, find cos A and tan A.
Answer
Step 1: From sin A = 7/25, we know opposite/hypotenuse = 7/25. Let opposite = 7k and hypotenuse = 25k. Step 2: Find adjacent using Pythagoras: adjacent² + opposite² = hypotenuse² → adjacent² + (7k)² =…
Evaluate: sin 30° + cos 60° - tan 45°
Answer
Step 1: Recall standard angle values: • sin 30° = 1/2 • cos 60° = 1/2 • tan 45° = 1 Step 2: Substitute values into expression: sin 30° + cos 60° - tan 45° = 1/2 + 1/2 - 1 Step 3: Calculate: = 1/2 + …
Find the value of: sin² 45° + cos² 45°
Answer
Step 1: Recall standard angle value: sin 45° = cos 45° = 1/√2 Step 2: Calculate sin² 45°: sin² 45° = (1/√2)² = 1/2 Step 3: Calculate cos² 45°: cos² 45° = (1/√2)² = 1/2 Step 4: Add them: sin² 45° + …
When do you use complementary angle relationships? Give an example with calculation.
Answer
Use complementary angle relationships when you know one angle and need to find trigonometric ratios of its complement (two angles that sum to 90°). Key relationships: sin θ = cos(90° - θ), cos θ = sin…
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