Trigonometry
Trigonometry
Introduction
Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of triangles.
Basic Functions
Sine (sin): In a right triangle, sin(θ) = opposite side / hypotenuse.
Cosine (cos): cos(θ) = adjacent side / hypotenuse.
Tangent (tan): tan(θ) = opposite side / adjacent side.
Reciprocal Functions
Cosecant (csc): csc(θ) = 1/sin(θ).
Secant (sec): sec(θ) = 1/cos(θ).
Cotangent (cot): cot(θ) = 1/tan(θ).
Pythagorean Identity
sin²(θ) + cos²(θ) = 1
Trigonometric Ratios in Different Quadrants
Angles are categorized into four quadrants: I (0° to 90°), II (90° to 180°), III (180° to 270°), and IV (270° to 360°).
The signs of the trigonometric functions change depending on the quadrant.
Applications
Used in various fields such as physics, engineering, computer graphics, and navigation.
Summary
Mastery of trigonometric functions and their relationships is essential for solving problems involving angles and distances.
Trigonometry
Introduction
Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of triangles.
Basic Functions
Sine (sin): In a right triangle, sin(θ) = opposite side / hypotenuse.
Cosine (cos): cos(θ) = adjacent side / hypotenuse.
Tangent (tan): tan(θ) = opposite side / adjacent side.
Reciprocal Functions
Cosecant (csc): csc(θ) = 1/sin(θ).
Secant (sec): sec(θ) = 1/cos(θ).
Cotangent (cot): cot(θ) = 1/tan(θ).
Pythagorean Identity
sin²(θ) + cos²(θ) = 1
Trigonometric Ratios in Different Quadrants
Angles are categorized into four quadrants: I (0° to 90°), II (90° to 180°), III (180° to 270°), and IV (270° to 360°).
The signs of the trigonometric functions change depending on the quadrant.
Applications
Used in various fields such as physics, engineering, computer graphics, and navigation.
Summary
Mastery of trigonometric functions and their relationships is essential for solving problems involving angles and distances.