Class 11 Maths NCERT Solutions: Trigonometric Functions

Chapter 3 - Samikaran aur Uttar

Trigonometric Functions ka ye chapter Class 11 ke liye bahut hi mahatvapurn hai. Yahaan par hum angles aur triangles ke beech ke sambandhon ko padhenge. Is chapter mein students ko milenge:

• Basic trigonometric ratios aur unki identities
• Degree aur radian measure
• Trigonometric functions ke graphs
• Important formulas aur unka application

Niche diye gaye detailed solutions se aap har concept ko asani se samjh paayenge.

Links for Chapter-wise Download NCERT Solution for Class 11 गणितII in hindi Language

Here we have provided NCERT Solution for Class 11 गणितII in hindi Language, Just select the chapters below to get solution of the same:

शांकव परिच्छेदन

त्रिविमीय ज्यामिति का परिचय

सीमा और अवकलज

गणितीय विवेचन

सांख्यिकी

प्रायिकता

Trigonometric Functions - Complete NCERT Solutions

Yeh solutions Class 11 Maths ke Chapter 3 ke liye designed kiye gaye hain. Har question ko step-by-step explain kiya gaya hai taki students deeply concept ko grasp kar saken. Solutions Hinglish language mein hain jisse samajhna aasan ho.

1. Basic Concepts aur Definitions

Sabse pehle, hum trigonometric ratios ke bare mein padhenge. Right-angled triangle mein, teen basic ratios hote hain: sine, cosine, aur tangent. Inhe aise define karte hain:

• sin θ = opposite side / hypotenuse
• cos θ = adjacent side / hypotenuse
• tan θ = opposite side / adjacent side

Inhi se hum derive karte hain cosec, sec, aur cot ratios. Ye sabhi ratios ek dusre se related hain through trigonometric identities.

2. Degree aur Radian Measure

Angles ko measure karne ke do common tarike hain: degrees aur radians. Ek complete circle 360 degrees ya 2π radians ke barabar hota hai. Conversion formula ye hai: radians = (π/180) × degrees. Is conversion ka use karke hum problems solve karte hain.

Example: 60 degrees ko radians mein convert karenge.
Solution: Radians = (π/180) × 60 = π/3 radians.

3. Trigonometric Functions ke Graphs

Har trigonometric function ka apna unique graph hota hai. Sine aur cosine functions periodic hote hain with period 2π. Tangent function ka period π hota hai. In graphs ko samajhna important hai kyunki ye functions ki behavior dikhate hain.

Graph plotting karte waqt hum domain aur range par dhyan dete hain. For example, sine function ki range -1 se 1 tak hoti hai.

4. Important Trigonometric Identities

Kuch basic identities jo har student ko yaad rakhni chahiye:

• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = cosec²θ

In identities ka use karke hum complex problems ko simplify kar sakte hain. Practice se ye formulas automatically yaad ho jaati hain.

5. Practice Problems with Solutions

Ab hum kuch important NCERT problems ke solutions dekhenge.

Problem: Agar sin A = 3/5, to cos A aur tan A ki value find kariye.
Solution: Hum jaante hain sin²A + cos²A = 1
Isliye, cos²A = 1 - sin²A = 1 - (9/25) = 16/25
So, cos A = 4/5 (positive lenge kyunki A first quadrant mein hai as per question)
Ab tan A = sin A / cos A = (3/5) / (4/5) = 3/4

6. Tips for Exam Preparation

• Sabse pehle, all basic formulas yaad karein.
• Regular practice karein different types of problems solve karke.
• Previous years ke question papers solve karein.
• Graphs ko achhe se samjhein aur unki plotting practice karein.
• Doubts ho to immediately teacher se puchen ya reference books check karein.

In solutions se aapko trigonometric functions ke concepts clear ho jaayenge. Har step ko carefully follow karein aur khud se practice karein. Confidence ke saath apne exams ki taiyaari karein.