maths.free › Trigonometry

Trigonometry

Angles, the unit circle, identities and trig equations.

Àwọn Àkọsílẹ̀

Introductory The unit circle Exact values of sine and cosine at the special angles. sin(pi/3) Core Trigonometric equations Reference angles and the infinitely many solutions. sin(x) = 1/2 Core Trigonometric identities Pythagorean, double-angle and sum identities, verified by simplification. simplify sin(x)^2 + cos(x)^2 Introductory Degrees and radians Two ways to measure an angle, and converting between them. 30 degrees to radians Core Right-triangle trigonometry (SOH-CAH-TOA) Sine, cosine and tangent as side ratios, and solving right triangles. hypotenuse of 5 and 12 Core Law of sines and law of cosines Solving any triangle from three pieces of information. triangle 5 7 with angle 60 Core Graphs of sine, cosine and tangent Amplitude, period, phase shift and the shape of periodic motion. y = sin(x) + cos(2x) Core Inverse trigonometric functions arcsin, arccos, arctan (which angle has this ratio) and their derivatives. derivative of arctan(x)

Trigonometry is the geometry of the circle written as functions. Exact values from the unit circle, equations with infinitely many solutions, and the identities that make them tame.

Àwọn ìwé-ìwé mìíràn

Trigonometric Identities and Equations

Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions Introduction to Trigonometric Identities and Equations Simplifying and Verifying Trigonometric Identities Sum and Difference Identities Double-Angle, Half-Angle, and Reduction Formulas Sum-to-Product and Product-to-Sum Formulas Solving Trigonometric Equations Modeling with Trigonometric Functions

Trigonometric Functions

Introduction to Trigonometric Functions Unit Circle: Sine and Cosine Functions The Other Trigonometric Functions Right Triangle Trigonometry

Periodic Functions

Introduction to Periodic Functions Graphs of the Sine and Cosine Functions Graphs of the Other Trigonometric Functions

Further Applications of Trigonometry

Introduction to Further Applications of Trigonometry Non-right Triangles: Law of Sines Non-right Triangles: Law of Cosines Polar Coordinates Polar Coordinates: Graphs Polar Form of Complex Numbers Parametric Equations Parametric Equations: Graphs Vectors

The functions

Trigonometry Trigonometric functions Radian Sine and cosine Tangent (trigonometry)Inverse trigonometric functions Hyperbolic functions

Identities and triangles

List of trigonometric identities Pythagorean trigonometric identity Law of sines Law of cosines Law of tangents Solution of triangles Angle addition formula Double-angle formula Small-angle approximation

Awọn ẹkọ diẹ ninu awọn wọnyi ni a ṣe atunṣe lati awọn ọrọ ti o ṣii: OpenStax Algebra and Trigonometry 2e, OpenStax Precalculus 2e, Wikipedia. Àwọn ojú-ìwé ìwé-ìwé fún àwọn àwọn ìṣàmúlò-ètò àti àwọn ìṣàmúlò-ètò.

Àwọn àmì-ìwé tí a lo níbẹ̀

Tẹ àwọn àmì-ìwé fún ìṣàfarawé fún àwọn ìṣàmúlò-ètò, àwòrán, àti àwọn àmì-ìwé àwọn àmì-ìwé.

Àwọn Àtòjọ-ẹ̀yàn

Why radians instead of degrees?

A radian is the angle whose arc equals the radius, so it is a pure ratio rather than an arbitrary 1/360 of a turn. With radians the derivative of sin x is exactly cos x; with degrees a factor of π/180 appears everywhere.

Why does sin x = 1/2 have infinitely many solutions?

Sine repeats every full turn, and within one turn it reaches 1/2 twice (at π/6 and 5π/6). Add any whole number of turns to either and it is still true.

How do I remember the exact values?

Two triangles: the 45-45-90 with sides 1, 1, √2 and the 30-60-90 with sides 1, √3, 2. Every value for 30°, 45° and 60° is a ratio of those sides; symmetry gives the rest of the circle.

Ní àwọn ààyè rẹ̀?
Ṣàfihàn àti àwòrán nínú ojú-ìwé ìṣàmúlò-ètò: àwọn ìsẹ̀ gbogbo, àwòrán, àwọn à Àwọn Àwọn Àkọ́lé →

Àwọn ìṣàmúlò-ètò mìíràn

＋ Arithmetic 𝑥 Algebra △ Geometry ƒ Precalculus σ Statistics & Probability ⊢ Discrete Math & Logic ∫ Calculus ⊞ Linear Algebra ℕ Number Theory ẏ Differential Equations ∇ Multivariable Calculus ε Real Analysis ⋔ Combinatorics & Graph Theory ∈ Set Theory & Logic 𝔾 Abstract Algebra 𝑃 Probability Theory ≈ Numerical Methods ℂ Complex Analysis ◎ Topology μ Measure Theory ‖·‖ Functional Analysis κ Differential Geometry π₁ Algebraic Topology → Category Theory ∂ Partial Differential Equations ≋ Fluid Dynamics ∞ Frontiers