Introduction To Trigonometry

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Step 1: Find hypotenuse using Pythagoras theorem → AC = √(AB² + BC²) = √(9 + 16) = √25 = 5 cm Step 2: Apply definitions with respect to angle A: • sin A = opposite/hypotenuse = BC/AC = 4/5 • cos A = a…

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Step 1: Draw right triangle with opposite = 12k, hypotenuse = 13k Step 2: Find adjacent using Pythagoras theorem → adjacent² + opposite² = hypotenuse² adjacent² + (12k)² = (13k)² → adjacent² = 169k² -…

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Step 1: Consider right triangle with hypotenuse = h, opposite = o, adjacent = a Step 2: Write trigonometric ratios: sin θ = o/h, cos θ = a/h Step 3: Square both ratios: sin²θ = o²/h², cos²θ = a²/h² St…

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Step 1: Given cos A = 7/25, so adjacent = 7k, hypotenuse = 25k Step 2: Find opposite using Pythagoras theorem: opposite² + adjacent² = hypotenuse² opposite² = (25k)² - (7k)² = 625k² - 49k² = 576k² opp…

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Step 1: Recall standard angle values: • sin 30° = 1/2 (from 30-60-90 triangle) • cos 60° = 1/2 (complementary to sin 30°) • tan 45° = 1 (from 45-45-90 triangle) Step 2: Substitute values: sin 30° + co…

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Step 1: Express left side in terms of sin θ and cos θ: tan θ + cot θ = sin θ/cos θ + cos θ/sin θ Step 2: Find common denominator: = (sin²θ + cos²θ)/(sin θ cos θ) Step 3: Apply fundamental identity (si…

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Step 1: Use the complementary angle relationship: tan θ = cot (90° - θ) Step 2: Express tan 2A as cot: tan 2A = cot (90° - 2A) Step 3: Set up equation: cot (90° - 2A) = cot (A - 18°) Step 4: Since cot…

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Step 1: Find QR using Pythagoras theorem: PR² = PQ² + QR² 13² = 5² + QR² 169 = 25 + QR² QR² = 144, so QR = 12 cm Step 2: For angle P, identify sides: Opposite = QR = 12 cm, Adjacent = PQ = 5 cm, Hypot…