Trigonometry Basics

Trigonometry

Definitions

• Trigonometry: Branch of mathematics dealing with relationships between the sides and angles of triangles.
• Right Triangle: A triangle with one right angle (90 degrees).

Key Concepts

• Angles: Measured in degrees, radians, or revolutions.
• Trigonometric Ratios: Relationships between sides and angles of a right triangle.
• Unit Circle: A circle with a radius of 1 unit, used to define trigonometric functions.

Trigonometric Functions

• Sine (sin): Opposite side / Hypotenuse
• Cosine (cos): Adjacent side / Hypotenuse
• Tangent (tan): Opposite side / Adjacent side
• Cotangent (cot): Adjacent side / Opposite side
• Secant (sec): Hypotenuse / Adjacent side
• Cosecant (csc): Hypotenuse / Opposite side

Identities and Formulas

• Pythagorean Identity: sin^2(A) + cos^2(A) = 1
• Sum and Difference Formulas: sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
• Double Angle Formulas: sin(2A) = 2sin(A)cos(A), cos(2A) = cos^2(A) - sin^2(A)

Applications

• Triangles: Solving right triangles, oblique triangles, and trigonometric equations.
• Waves and Cycles: Modeling periodic phenomena, such as sound, light, and electrical signals.
• Analytic Geometry: Using trigonometry to solve problems in coordinate geometry.

Important Theorems

• Law of Sines: a / sin(A) = b / sin(B) = c / sin(C) (relates sides and angles of a triangle)
• Law of Cosines: a^2 = b^2 + c^2 - 2bc * cos(A) (relates sides and angles of a triangle)

Trigonometry Definitions

• Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles.
• A right triangle is a triangle with one right angle (90 degrees).

Key Concepts

• Angles can be measured in degrees, radians, or revolutions.
• Trigonometric ratios describe the relationships between the sides and angles of a right triangle.
• The unit circle is a circle with a radius of 1 unit, used to define trigonometric functions.

Trigonometric Functions

• Sine (sin) is the ratio of the opposite side to the hypotenuse.
• Cosine (cos) is the ratio of the adjacent side to the hypotenuse.
• Tangent (tan) is the ratio of the opposite side to the adjacent side.
• Cotangent (cot) is the ratio of the adjacent side to the opposite side.
• Secant (sec) is the ratio of the hypotenuse to the adjacent side.
• Cosecant (csc) is the ratio of the hypotenuse to the opposite side.

Identities and Formulas

• The Pythagorean identity is sin^2(A) + cos^2(A) = 1.
• The sum and difference formulas describe the relationships between the sine and cosine of the sum or difference of two angles.
• The double angle formulas describe the relationships between the sine and cosine of twice an angle.

Applications

• Trigonometry can be used to solve right triangles, oblique triangles, and trigonometric equations.
• Trigonometry can be used to model periodic phenomena, such as sound, light, and electrical signals.
• Trigonometry can be used in coordinate geometry to solve problems.

Important Theorems

• The Law of Sines states that a / sin(A) = b / sin(B) = c / sin(C) for a triangle with sides a, b, and c, and angles A, B, and C.
• The Law of Cosines states that a^2 = b^2 + c^2 - 2bc * cos(A) for a triangle with sides a, b, and c, and angle A.

Test your knowledge of trigonometry, including definitions, key concepts, and trigonometric functions. Learn about right triangles, angles, and trigonometric ratios.