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8.Graphs of Trigonometric Functions
Class 11 • Mathematics • NCERT
Graphs of Trigonometric Functions
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This lesson introduces the graphs of basic trigonometric functions as per NCERT Class 11. Students learn how to draw and understand the graphs of sin x, cos x, and tan x using standard angle values.
Lesson Objectives
- Understand how trigonometric graphs are drawn.
- Draw the graph of sin x.
- Draw the graph of cos x.
- Understand the basic shape of tan x.
1. Graph of y = sin x
The graph of y = sin x is drawn using standard values of x.
Key points (NCERT):
x = 0, π/2, π, 3π/2, 2π
sin x = 0, 1, 0, −1, 0
x = 0, π/2, π, 3π/2, 2π
sin x = 0, 1, 0, −1, 0
2. Graph of y = cos x
The graph of y = cos x is also periodic and smooth.
Key points:
x = 0, π/2, π, 3π/2, 2π
cos x = 1, 0, −1, 0, 1
x = 0, π/2, π, 3π/2, 2π
cos x = 1, 0, −1, 0, 1
3. Graph of y = tan x
The graph of y = tan x is different from sin x and cos x.
Important NCERT points:
• tan x is not defined at x = π/2, 3π/2
• Graph increases continuously between asymptotes
• tan x is not defined at x = π/2, 3π/2
• Graph increases continuously between asymptotes
4. Important Observations
• sin x and cos x lie between −1 and 1
• sin x and cos x are periodic with period 2π
• tan x is periodic with period π
• sin x and cos x are periodic with period 2π
• tan x is periodic with period π
Practice Questions (NCERT)
- Write the value of sin 0.
- Write the value of cos 0.
- What is the period of sin x?
- What is the period of cos x?
- What is the period of tan x?
- Is tan x defined at π/2?
- Between which values does sin x lie?
- Between which values does cos x lie?
- Which function has vertical asymptotes?
- Are these graphs part of NCERT syllabus?
✅ Show Answer Key
- 0
- 1
- 2π
- 2π
- π
- No
- −1 to 1
- −1 to 1
- tan x
- Yes
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