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7.Trigonometric Functions – Basics
Class 11 • Mathematics • NCERT
Trigonometric Functions – Basics
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This lesson introduces the basic idea of trigonometric functions as per NCERT Class 11. Students learn angles, trigonometric ratios in a right-angled triangle, and the basic trigonometric functions with simple examples.
Lesson Objectives
- Understand angles and their measurement.
- Define trigonometric ratios.
- Learn basic trigonometric functions.
- Apply ratios to simple problems.
1. Angles and Right-Angled Triangle
Trigonometry deals with the relationship between the sides and angles of a right-angled triangle.
In a right-angled triangle:
• One angle is 90°
• The longest side is called the hypotenuse
• One angle is 90°
• The longest side is called the hypotenuse
2. Trigonometric Ratios
The ratios of sides of a right-angled triangle with respect to an acute angle are called trigonometric ratios.
For an angle θ:
sin θ = (Opposite side) / (Hypotenuse)
cos θ = (Adjacent side) / (Hypotenuse)
tan θ = (Opposite side) / (Adjacent side)
sin θ = (Opposite side) / (Hypotenuse)
cos θ = (Adjacent side) / (Hypotenuse)
tan θ = (Opposite side) / (Adjacent side)
3. Trigonometric Functions
The trigonometric ratios are also called trigonometric functions.
Basic trigonometric functions:
• sin θ
• cos θ
• tan θ
• sin θ
• cos θ
• tan θ
4. Values of Trigonometric Functions (Intro)
Trigonometric functions have fixed values for some standard angles.
Examples:
sin 0° = 0
sin 90° = 1
cos 0° = 1
cos 90° = 0
sin 0° = 0
sin 90° = 1
cos 0° = 1
cos 90° = 0
Practice Questions (NCERT)
- What is a right-angled triangle?
- Name the longest side of a right-angled triangle.
- Define sin θ.
- Define cos θ.
- Define tan θ.
- What are trigonometric ratios?
- Write sin 0°.
- Write cos 0°.
- Write sin 90°.
- Are trigonometric ratios functions?
✅ Show Answer Key
- A triangle with one angle equal to 90°.
- Hypotenuse.
- Opposite side divided by hypotenuse.
- Adjacent side divided by hypotenuse.
- Opposite side divided by adjacent side.
- Ratios of sides of a right-angled triangle.
- 0
- 1
- 1
- Yes.
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