Holiday Readings at eBooks.com









Holiday Readings at eBooks.com






Trigonometry is the study of triangles with respect to their sides and angles and with the functions of those angles. It is extremely important in all scientific fields.


Trigonometric Relationships

Trigonometric Relationships
Trigonometric Relationships

Right Triangular Ratios

Triangular Angles
Triangular Angles

\(sin\,α=\frac{a}{c}\) \(cos\,α=\frac{b}{c}\) \(tan\,α=\frac{a}{b}\) \(csc\,α=\frac{c}{a}\) \(sec\,α=\frac{c}{b}\) \(cot\,α=\frac{b}{a}\)

\(sin\,β=\frac{b}{c}\) \(cos\,β=\frac{a}{c}\) \(tan\,β=\frac{b}{a}\) \(csc\,β=\frac{c}{b}\) \(sec\,β=\frac{c}{a}\) \(cot\,β=\frac{a}{b}\)



Cofunction Theorem (Triangular)


\(sin\,α=cos\,β\) \(cos\,α=sin\,β\) \(tan\,α=cot\,β\) \(csc\,α=sec\,β\) \(sec\,α=csc\,β\) \(cot\,α=tan\,β\)




Circular Ratios

Circular Angles
Circular Angle

\(sin\,θ=\frac{y}{r}\) \(cos\,θ=\frac{x}{r}\) \(tan\,θ=\frac{y}{x}\) \(csc\,θ=\frac{r}{y}\) \(sec\,θ=\frac{r}{x}\) \(cot\,θ=\frac{x}{y}\)



Cofunction Theorem (Circular)


\(sin\,θ=cos\,(\frac{π}{2}-θ)\) \(cos\,θ=sin\,(\frac{π}{2}-θ)\) \(tan\,θ=cot\,(\frac{π}{2}-θ)\) \(csc\,θ=sec\,(\frac{π}{2}-θ)\) \(sec\,θ=csc\,(\frac{π}{2}-θ)\) \(cot\,θ=tan\,(\frac{π}{2}-θ)\) 




Reciprocal Identities


\(sin\,θ=\frac{1}{csc\,θ}\) \(cos\,θ=\frac{1}{sec\,θ}\) \(tan\,θ=\frac{1}{cot\,θ}\) \(csc\,θ=\frac{1}{sin\,θ}\) \(sec\,θ=\frac{1}{cos\,θ}\) \(cot\,θ=\frac{1}{tan\,θ}\)




Ratio Identities


\(sin\,θ=cos\,θ\,tan\,θ=\frac{cos\,θ}{cot\,θ}\) \(cos\,θ=sin\,θ\,cot\,θ=\frac{sin\,θ}{tan\,θ}\) \(tan\,θ=sin\,θ\,sec\,θ=\frac{sin\,θ}{cos\,θ}\) \(csc\,θ=sec\,θ\,cot\,θ=\frac{cot\,θ}{cos\,θ}\) \(sec\,θ=csc\,θ\,tan\,θ=\frac{tan\,θ}{sin\,θ}\) \(cot\,θ=cos\,θ\,csc\,θ=\frac{cos\,θ}{sin\,θ}\)




Pythagorean Identities


\(sin^2\,θ+cos^2\,θ=1\) \(sin^2\,θ=1-cos^2\,θ\) \(cos^2\,θ=1-sin^2\,θ\) \(tan^2\,θ=sec^2\,θ-1\) \(cot^2\,θ=csc^2\,θ-1\) \(sec^2\,θ=1+tan^2\,θ\) \(csc^2\,θ=1+cot^2\,θ\)




Function Conversions



Sum and Difference Formulas



Inverse Identities



Miscellaneous Identities



The Law of Sines



The Law of Cosines



The Law of the Cotangent



Reciprocal Identities



Double-Angle Formulas



Half-Angle Formulas



Product to Sum Formulas



Sum to Product Formulas



Reduction Formulas