Trigonometry Table Class 11: Standard Values and Formulas

Trigonometry Table Class 11: Standard Values and Formulas

Trigonometry Table Class 11: Standard Values of Trigonometric Ratios

Trigonometry is an important branch of mathematics that deals with the relationship between the angles and sides of a triangle. In Class 11, students learn the standard values of trigonometric ratios, which are essential for solving various mathematical problems.

What is a Trigonometry Table?

A trigonometry table contains the standard values of the six trigonometric ratios for commonly used angles. These values help students solve trigonometric equations quickly without performing lengthy calculations.

The six trigonometric ratios are:

  • Sine (sin)
  • Cosine (cos)
  • Tangent (tan)
  • Cotangent (cot)
  • Secant (sec)
  • Cosecant (cosec)

Trigonometry Table (Standard Angles)

Angle (θ)0°30°45°60°90°
sin θ01/21/√2√3/21
cos θ1√3/21/√21/20
tan θ01/√31√3Not Defined
cosec θNot Defined2√22/√31
sec θ12/√3√22Not Defined
cot θNot Defined√311/√30

Trigonometric Ratios Formulas

For a right-angled triangle:

  • sin θ = Perpendicular / Hypotenuse
  • cos θ = Base / Hypotenuse
  • tan θ = Perpendicular / Base
  • cosec θ = Hypotenuse / Perpendicular
  • sec θ = Hypotenuse / Base
  • cot θ = Base / Perpendicular

Important Trigonometric Identities

1. Pythagorean Identity

sin²θ + cos²θ = 1

2. Tan-Sec Identity

1 + tan²θ = sec²θ

3. Cot-Cosec Identity

1 + cot²θ = cosec²θ

Tips to Remember the Trigonometry Table

For Sine Values

Use the formula:

sin θ = √n / 2

where n = 0, 1, 2, 3, 4

Thus:

  • sin 0° = √0/2 = 0
  • sin 30° = √1/2 = 1/2
  • sin 45° = √2/2 = 1/√2
  • sin 60° = √3/2
  • sin 90° = √4/2 = 1

For Cosine Values

Reverse the sine values:

  • cos 0° = 1
  • cos 30° = √3/2
  • cos 45° = 1/√2
  • cos 60° = 1/2
  • cos 90° = 0

Applications of Trigonometry

Trigonometry is used in:

  • Engineering
  • Architecture
  • Navigation
  • Astronomy
  • Physics
  • Surveying
  • Computer Graphics