Trigonometrical Ratios of Complementary Angles
Complementary Angles
Complementary Angles
In the right-angled triangle △OPM, the complement of the angle θ is (90° − θ).
💡 With respect to θ, the perpendicular side is PM and the base is OM.
💡 With respect to (90° − θ), the perpendicular side is OM and the base is PM.
Ratios with respect to θ | Ratios with respect to (90° − θ) |
|---|---|
| sin θ = | sin (90° − θ) = |
| cos θ = | cos (90° − θ) = |
| tan θ = | tan (90° − θ) = |
| cosec θ = | cosec (90° − θ) = |
| sec θ = | sec (90° − θ) = |
| cot θ = | cot (90° − θ) = |
From the table, we get the following complementary angle relations:
👉 sin θ = cos (90° − θ)
👉 cos θ = sin (90° − θ)
👉 tan θ = cot (90° − θ)
👉 cot θ = tan (90° − θ)
👉 cosec θ = sec (90° − θ)
👉 sec θ = cosec (90° − θ)
Easy Way to Remember
When the angle changes from θ to (90° − θ), each trigonometrical ratio changes into its co-ratio:
| Ratio | Co-ratio |
|---|---|
| sin | cos |
| tan | cot |
| sec | cosec |
For example:
👉 sin (90° − θ) = cos θ
👉 tan (90° − θ) = cot θ
👉 sec (90° − θ) = cosec θ