11th Math Chapter 10 || Ex 10.1 || Sir Ikram || Learn For Pakistan

Welcome to your own classroom — Learn For Pakistan — where mathematics is taught in the easiest, cleanest and most understandable way for every student of Punjab.

In this lecture, we solve Chapter 10 – Trigonometric Functions & Identities – Question No. 1, where we find the values of angles like:

✔ sin 110°
✔ cos (–123°)
✔ sin 1180°, cos 1260°, etc.

WITHOUT using a calculator — only with concept + quadrant + identities.

This is an important short question for all Punjab Boards (Lahore, Multan, Gujranwala, Sahiwal, DG Khan, Sargodha, Faisalabad, Rawalpindi, Bahawalpur, Federal Board).

🔥 What You Will Learn in This Lecture

This lecture is full of concepts, including:

✔ 1. How to reduce big angles

• Convert 1100°, 1180°, 1260°, etc. using
→ 360° rule
→ 180° rule
So the angle becomes small and easy.

✔ 2. How to work with negative angles

• cos(–123°) = cos(123°) (because cos is even)
• sin(–θ) = –sin(θ) (odd function)

✔ 3. Complete Quadrant Concept

You will fully understand:

1st Quadrant → All are positive

2nd Quadrant → Only Sin & Cosec positive

3rd Quadrant → Only Tan & Cot positive

4th Quadrant → Only Cos & Sec positive

This method helps you find the sign of any trigonometric ratio easily.

✔ 4. How to move angle into another quadrant

When we add or subtract 90°, 180°, or 360°:

• Add 90° → Angle moves to next quadrant
• Add 180° → Angle moves to opposite quadrant
• Add 360° → Angle returns to same quadrant

You also learn when the trigonometric function changes (like sin becomes cos, cos becomes –sin, etc.).

✔ 5. How to find the reference angle

Find the basic acute angle (like 30°, 45°, 60°) and then apply the sign from the correct quadrant.

✔ 6. Pure exam-targeted solution

Every question is solved step-by-step with clear logic, perfect for short questions and MCQs.

🌟 Why This Lecture is Important

✔ Highly important for Punjab Boards
✔ Very common question in short questions
✔ Perfect for preparation of Mid-term + Final term
✔ You will learn how to solve any angle without calculator
✔ Very easy and fast method — even weak students can master it

🌟 Why Students Love This Classroom

This is not just a YouTube channel.
This is your classroom.

Here, every student can learn:

✔ In easy words
✔ With simple steps
✔ With visual logic
✔ With real understanding, NOT memorization
✔ With practical examples
✔ With full clarity and confidence

Even an average or weak student becomes strong when the method is easy.

🇵🇰 My Mission for the Students of Pakistan

I, Sir Ikram Raheem, teach with a purpose:

• No student should fail
• Every student should understand, not cram
• Every student should work for their future, family and Pakistan
• Give students real confidence
• Build strong concepts, not shortcuts
• Create a generation that learns, thinks and grows
• Replace reels with education
• Give real freedom through knowledge

Join the mission of Educated Pakistan.

📢 What You Should Do

👉 Subscribe to join the classroom
👉 Like the video to support the mission
👉 Comment your questions — this class is for you
👉 Share with your friends — help them pass
👉 Watch full lecture for perfect understanding

Your success is my mission.
Your education is Pakistan’s strength.
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