Trigonometry: Tables and Formulas

Trigonometry is derived from Greek word trigonon, Which means “triangle” and metron, Means “measure”. It is a branch of mathematics that studies relationships between side lengths and angles of triangles. Trigonometry is applied in areas such as geodesy, surveying, celestial mechanics, and navigation. Trigonometry is known for its many identities, which are equations used for rewriting trigonometrical expressions to solve equations, to find a more useful expression, or to discover new relationships.

The trigonometry angles which are commonly used in trigonometry problems are 0°,30°,45°,60° and 90°. The trigonometric ratios such as sine, cosine and tangent of these angles are easy to memorize. We will also show the table where all the ratios and their respective angle’s values are mentioned. To find these angles we have to draw a right-angled triangle, in which one of the acute angles will be the corresponding trigonometry angle. These angles will be defined with respect to the ratio associated with it.

Trigonometry-triangle

Sin θ = Perpendicular/Hypotenuse

or θ = sin-1 (P/H)

Similarly,

θ = cos-1 (Base/Hypotenuse)

θ = tan-1 (Perpendicular/Base)

Trigonometry Table

The below table sows common angles which are used to solve many trigonometric problems based on trigonometric ratios.

Angles 30° 45° 60° 90°
Sin θ 0 ½ 1/√2 √3/2 1
Cos θ 1 √3/2 1/√2 ½ 0
Tan θ 0 1/√3 1 √3
Cosec θ 2 √2 2/√3 1
Sec θ 1 2/√3 √2 2
Cot θ √3 1 1/√3 0

Formulas

The Trigonometric formulas or Identities are the equations which are true in the case of Right-Angled Triangles. Some of the special Pythagorean Identities are as given below:

  • sin ² θ + cos ² θ = 1
  • tan 2 θ + 1 = sec2 θ
  • cot2 θ + 1 = cosec2 θ
  • sin 2θ = 2 sin θ cos θ
  • cos 2θ = cos² θ – sin² θ
  • tan 2θ = 2 tan θ / (1 – tan² θ)
  • cot 2θ = (cot² θ – 1) / 2 cot θ