Introduction to Trigonometry — Flashcards
Karnataka Board · Class 10 · Mathematics
20 flashcards for Introduction to Trigonometry (Karnataka Board Class 10 Mathematics) to test yourself on key terms and facts.
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In right triangle ABC, if AB = 24 cm, BC = 7 cm, and angle B = 90°, find sin A and cos A.
Answer
Step 1: Find AC using Pythagoras theorem AC² = AB² + BC² = 24² + 7² = 576 + 49 = 625 AC = √625 = 25 cm Step 2: Apply trigonometric ratios sin A = opposite/hypotenuse = BC/AC = 7/25 = 0.28 cos A = adj…
If tan θ = 4/3, find all other trigonometric ratios.
Answer
Step 1: Draw right triangle where opposite = 4k, adjacent = 3k Step 2: Find hypotenuse using Pythagoras hypotenuse² = (4k)² + (3k)² = 16k² + 9k² = 25k² hypotenuse = 5k Step 3: Calculate all ratios s…
Calculate: sin² 30° + cos² 30°
Answer
Step 1: Recall values from table sin 30° = 1/2 cos 30° = √3/2 Step 2: Square each value sin² 30° = (1/2)² = 1/4 cos² 30° = (√3/2)² = 3/4 Step 3: Add them sin² 30° + cos² 30° = 1/4 + 3/4 = 4/4 = 1 N…
In triangle ABC, right-angled at B, if tan A = 1, find the value of 2 sin A cos A.
Answer
Step 1: Since tan A = 1, opposite = adjacent Let AB = BC = k (equal sides) Step 2: Find hypotenuse AC = √(AB² + BC²) = √(k² + k²) = k√2 Step 3: Calculate sin A and cos A sin A = BC/AC = k/(k√2) = 1/…
Find the height of a tower if its shadow is 50 m long and the angle of elevation of the sun is 30°.
Answer
Step 1: Set up the problem Let height of tower = h Shadow length = 50 m Angle of elevation = 30° Step 2: Apply trigonometry tan 30° = height/shadow 1/√3 = h/50 Step 3: Solve for h h = 50/√3 = 50√3/3…
Solve: (1 + tan² A) = ?
Answer
Step 1: Start with fundamental identity sin² A + cos² A = 1 Step 2: Divide throughout by cos² A sin² A/cos² A + cos² A/cos² A = 1/cos² A Step 3: Simplify using ratio definitions (sin A/cos A)² + 1 =…
If sin θ = 3/5, find cos θ and tan θ without using a calculator.
Answer
Step 1: Use the identity sin² θ + cos² θ = 1 (3/5)² + cos² θ = 1 9/25 + cos² θ = 1 cos² θ = 1 - 9/25 = 16/25 Step 2: Find cos θ cos θ = ±√(16/25) = ±4/5 Since θ is acute, cos θ = 4/5 Step 3: Find ta…
Calculate: cos 60° × sin 30° + sin 60° × cos 30°
Answer
Step 1: Substitute special angle values cos 60° = 1/2, sin 30° = 1/2 sin 60° = √3/2, cos 30° = √3/2 Step 2: Calculate each term cos 60° × sin 30° = (1/2) × (1/2) = 1/4 sin 60° × cos 30° = (√3/2) × (√…
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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