Consider a right-angled triangle Δ ABC. We know the existing trigonometric relationships between the opposite, adjacent sides and the hypotenuse of the triangle.

sin θ =

cos θ =

tan θ =

Now we look at some other trigonometric relationships:

sin (90 – θ) = = cos θ

cos (90 – θ) = = sin θ

Hence sin (90 – θ) = cos θ, and

cos (90 – θ) = sin θ

tan θ =

We define three inverse trigonometric ratios as:

cosecant angle = cosec θ =

secant angle = sec θ =

cotangent angle = cot θ =

Hence cot θ =

Therefore tan (90 – θ) = = cot θ

Sine and cosine are called complementary ratios. Similarly, tangent and co-tangent are called complementary ratios.

## Summary of Trigonometric Relationships

sin θ = cos (90 – θ)

cos θ = sin (90 – θ)

tan θ = cot (90 – θ)

cosec θ = = sec (90 – θ)

sec θ = = cosec (90 – θ)

cot θ = = tan (90 – θ)

Hence, in a right-angled triangle, θ and (90 – θ) are complementary angles. When two angles are complementary, we can find their complementary ratios given one of the angles.

Let us now look at some examples of trigonometric relationships.