Complementary Angles
What is Complementary Angles?
Two angles are called complementary if the sum of their measures is 90 degrees.
Key formula / rule: Complementary Angle Definition
Key points
- Define complementary angles and identify them.
- Calculate the measure of a complementary angle given one angle.
- Apply the concept of complementary angles in solving geometric problems.
- Utilize trigonometric identities involving complementary angles to simplify expressions.
Common exam trap
Confusing complementary angles (sum 90°) with supplementary angles (sum 180°).
Definitions
- Term
Complementary Angles
- Meaning
Two angles are called complementary if the sum of their measures is 90 degrees.
- Term
Complement
- Meaning
An angle is the complement of another angle if their sum is 90 degrees.
Learning objectives
Define complementary angles and identify them.
Calculate the measure of a complementary angle given one angle.
Apply the concept of complementary angles in solving geometric problems.
Utilize trigonometric identities involving complementary angles to simplify expressions.
Formulae
- Name
Complementary Angle Definition
- Note
Angles A and B are complementary.
- Expression
A + B = 90°
- Name
Sine-Cosine Complementary Relation
- Note
The sine of an angle equals the cosine of its complement.
- Expression
sin(θ) = cos(90° - θ)
- Name
Tangent-Cotangent Complementary Relation
- Note
The tangent of an angle equals the cotangent of its complement.
- Expression
tan(θ) = cot(90° - θ)
- Name
Secant-Cosecant Complementary Relation
- Note
The secant of an angle equals the cosecant of its complement.
- Expression
sec(θ) = cosec(90° - θ)
Prerequisites
Basic understanding of angles and their measurement.
Familiarity with basic geometric shapes, especially triangles.
Introduction to trigonometric ratios (sine, cosine, tangent, etc.).
Common mistakes
Confusing complementary angles (sum 90°) with supplementary angles (sum 180°).
Incorrectly applying trigonometric identities related to complementary angles.
Assuming angles are complementary without explicit information or geometric proof.
Keywords
complementary angles
90 degrees
trigonometry
geometry
right-angled triangle
sine
cosine
tangent
cotangent
secant
cosecant
Practice preview
Two complementary angles are in the ratio 4:5. Find the measure of the smaller angle.…
medium
Which of the following pairs of angles are complementary?…
easy
If an angle is represented by (2x + 10) degrees and its complementary angle is 30 degrees, what is the value of x?…
easy