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Trigonometry, coordinates, probability · Class 10

5 questions · English, हिन्दी, मराठी · answer key with explanations · 12 October 2026

NCERT: Class 10 Mathematics, Chapter 8: Introduction to Trigonometry; Class 10 Mathematics, Chapter 7: Coordinate Geometry; Class 10 Mathematics, Chapter 14: Probability. Our own questions in the chapter's style, drafted with AI help, every answer checked step by step; teacher review pending. Hindi and Marathi: translation - review pending.

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Trigonometry, coordinates, probability · English

Name: ____________________Date: ____________

sin 30° = ? (fraction or decimal)
tan 45° = ?
sin²θ + cos²θ = ?
How far apart are the points (0, 0) and (3, 4)?
A fair dice is rolled one time. What is the chance of getting an even number? (fraction)

1/2 — sin 30° = 1/2. Remember the table: sin 0°, 30°, 45°, 60°, 90° = 0, 1/2, 1/√2, √3/2, 1.
1 — tan 45° = sin 45° ÷ cos 45° = 1, because the two are equal at 45°.
1 — This identity holds for every angle θ: sin²θ + cos²θ = 1.
5 — Distance = √(3² + 4²) = √(9 + 16) = √25 = 5.
1/2 — Even numbers: 2, 4, 6, so 3 of the 6 outcomes. 3/6 = 1/2.

नाम: ____________________तारीख़: ____________

1/2 — sin 30° = 1/2। सारणी याद रखो: sin 0°, 30°, 45°, 60°, 90° = 0, 1/2, 1/√2, √3/2, 1।
1 — tan 45° = sin 45° ÷ cos 45° = 1, क्योंकि 45° पर दोनों बराबर हैं।
1 — यह सर्वसमिका हर कोण θ के लिए सही है: sin²θ + cos²θ = 1।
5 — दूरी = √(3² + 4²) = √(9 + 16) = √25 = 5।
1/2 — सम संख्याएँ: 2, 4, 6, यानी 6 में से 3। 3/6 = 1/2।

नाव: ____________________दिनांक: ____________

1/2 — sin 30° = 1/2. सारणी लक्षात ठेवा: sin 0°, 30°, 45°, 60°, 90° = 0, 1/2, 1/√2, √3/2, 1.
1 — tan 45° = sin 45° ÷ cos 45° = 1, कारण 45° ला दोन्ही समान असतात.
1 — ही नित्यसमानता प्रत्येक कोन θ साठी खरी आहे: sin²θ + cos²θ = 1.
5 — अंतर = √(3² + 4²) = √(9 + 16) = √25 = 5.
1/2 — सम संख्या: 2, 4, 6, म्हणजे 6 पैकी 3. 3/6 = 1/2.