Suppose we have two angles α = 50 ⁰ and β = 40 ⁰; If we add them, it gives us 90 ⁰, therefore, we say that α and β “complement each other”, that is, they are complementary angles.
The complementary angles are those that when added together result in 90⁰ (or π / 2 rad).
α and β are complementary since 62⁰ + 28⁰ = 90⁰
If we have two that are consecutive, the uncommon sides of both form a right angle.
Complementary angles in a right triangle
We know that the sum of the interior angles of any triangle is equal to 180⁰. Therefore, in a right triangle the two acute angles are complementary.
α + β = 90⁰
Trigonometric ratios of complementary angles
If α and β are complementary (α + β = 90⁰), then β = 90⁰ - α:
- without (90⁰ - α) = cos α
- cos (90⁰ - α) = without α
- tg (90⁰ - α) = ctg α
- csc (90⁰ - α) = sec α
- sec (90⁰ - α) = csc α
- ctg (90⁰ - α) = tg α