What are Trigonometry Ratios?

Trigonometry is useful in finding trigonometric functions. These functions are involved in

the form of an expression or equation. There are a few primary trigonometric ratios

such as sine, cosine, and tangent. Three more functions are formed using these primary

functions in trigonometries like cotangent, cosecant and secant. All the trigonometric

identities are made using these six trigonometric functions. Similarly, trigonometric

identities can be proved true for all the values which are given on both the left-hand side

and right-hand side of the equation. Mostly you might notice that the trigonometric

functions like sine, cosine, tangent, cotangent etc involve one or more than one angle.

List of Trigonometry Ratios

  • Sin O = Opposite side / Hypotenuse side
  • Cos O = Adjacent Side/ Hypotenuse side
  • Tan O = Opposite Side/ Adjacent Side
  • Cosec O = 1/ Sin O
  • Secant O = 1/ Cos O
  • Cotangent O = 1/ Tan O

Let’s Learn More About Trigonometric Identities?

Trigonometric identities include the side length and the angle of the triangle. It is true for

right-angled triangles. As mentioned in the above paragraph trigonometric identities

are made of the six trigonometric functions and those are defined by the sides of a right

angled triangle (Hypotenuse, base and opposite side. These trigonometric identities are

used to solve various trigonometry problems. You can also solve many complex

equations or formulas quickly using these identities. Here’s a list of a few of the

reciprocal trigonometric identities.

  • Cosec x is equal to 1/ sin x or sin x is equal to 1/cosec x , where x is the angle of

the right-angled triangle.

  • Secant x is equal to 1/ cos x or cos x is equal to 1/secant x, where x is the angle

of the right-angled triangle.

  • Cotangent x is equal to 1/ tangent x, tangent x is equal to 1/ cotangent x where x

is the angle of the right-angled triangle.

[List of Pythagorean Trigonometric Identities]

  • Sin 2 x + cos 2 x is equal to 1
  • 1 + tan 2 x is equal to sec 2 x
  • Cosec 2 x is equal to 1 + cot 2 x

[List of Ratio Trigonometric Identities]

  • Tan b is equal to sin b/cos b
  • Cot b is equal to cos b / sin b

[List of Trigonometric Identities of Opposite Angles]

  • Sin (-b) is equal to – sin b
  • Csc (-b) is equal to -Csc b
  • Cos (-b) is equal to Cos b
  • Sec (-b) is equal to Sec b
  • Cos (-b) is equal to Cos b
  • Tan (-b) is equal to – Tan b
  • Cot (-b) is equal to – Cot b

List of Trigonometric Identities of Complementary Angles

Let’s first understand what complementary angles are. Complementary angles are

angles having a sum of 90 degrees. So l et’s begin:

  • Sin (90 – b) is equal to Cos b
  • Csc (90 – b) is equal to Sec b
  • Cos (90 – b) is equal to Sin b
  • Sec (90 – b) is equal to Csc b
  • Tan (90 – b) is equal to Cot b
  • Cot ( 90 – ) is equal to Tan b

Trigonometric Identities of Supplementary Angles

Angles having a sum of 180 degrees are known as supplementary angles. Similarly,

when we can learn here the trig identities for supplementary angles.

  • sin (180°- v) = sin v
  • cos (180°- v) = -cos v
  • cosec (180°- v) = cosec v
  • sec (180°- v)= -sec v
  • tan (180°- v) = -tan v
  • cot (180°- v) = -cot v

List of Product-Sum Trigonometric Identities

  • Sin P + Sin Q is equal to 2 Sin(P+Q)/2 . Cos(P-Q)/2
  • Cos P + Cos Q is equal to 2 Cos(P+Q)/2 . Cos(P-Q)/2
  • Sin P – Sin Q is equal to 2 Cos(P+Q)/2 . Sin(P-Q)/2
  • Cos P – Cos Q is equal to -2 Sin(P+Q)/2 . Sin(P-Q)/2

List of Applications of Trigonometry

Let’s learn about various applications of Trigonometry in our daily life. As you know that

it is an interesting as well as complex topic, so to make it easy to understand cuemath

has created a live tutoring platform to help you grasp this concept better.

  • Trigonometry is used to determine the length or height of tall towers or


  • If you want to calculate the distance between the seashore and the sea,

trigonometry can help you.

  • Trigonometry is also used to calculate the separation between two celestial


There are many other applications of trigonometry, you can learn it on cuemath website.