Complementary Angles in Trigonometry
Let us observe the following figure.
In △ABC, ∠A + ∠C = 90°
So, we can say that ∠A and ∠C are complementary angles.
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Trigonometric Ratios of Complementary Angles
Let us consider △ABC again.
If ∠A = θ, then ∠C = 90° – θ
and
So, sin θ = cos (90° – θ)
Similarly, the following also holds true for 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)
Suppose we have to find the value of sin 52° – cos 38°.
We know that sin θ = cos (90° – θ)
sin 52° = cos (90° – 52°) = cos 38°
sin 52° – cos 38° = cos 38° – cos 38° = 0
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Complementary Angles
Two acute angles are said to be complementary angles if the sum of the angles equals 90° i.e., complementary angles are those angles whose sum adds up to 90°. In other words, we can say that the sum of complementary angles is 90°.
Complementary Angles are not just a term that is used in geometry as this also has some real-life applications. One such example is slicing a rectangular-shaped bread along the diagonal. We will get two right triangles, each with a pair of complementary angles. In this article, we will be learning about the definition of complementary angles, types of complementary angles, properties, and how to find the complement of an angle.
Table of Content
- What are Complementary Angles?
- Complementary Angles Examples
- Types of Complementary Angles
- Properties of Complementary Angles
- Complementary Angle Theorem
- Complementary Angles vs Supplementary Angles