Trigonometry

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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…

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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…

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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…

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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…

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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 =…

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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 + …

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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° + …

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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…