| symbol | latex code | explanation | |
|---|---|---|---|
sin(θ) | \sin(\theta) | Sine function | |
cos(θ) | \cos(\theta) | Cosine function | |
tan(θ) | \tan(\theta) | Tangent function | |
cot(θ) | \cot(\theta) | Cotangent function | |
sec(θ) | \sec(\theta) | Secant function | |
csc(θ) | \csc(\theta) | Cosecant function | |
sin⁻¹(x) | \sin^{-1}(x) | Inverse sine (arcsine) function | |
cos⁻¹(x) | \cos^{-1}(x) | Inverse cosine (arccosine) function | |
tan⁻¹(x) | \tan^{-1}(x) | Inverse tangent (arctangent) function | |
cot⁻¹(x) | \cot^{-1}(x) | Inverse cotangent (arccotangent) function | |
sec⁻¹(x) | \sec^{-1}(x) | Inverse secant (arcsecant) function | |
csc⁻¹(x) | \csc^{-1}(x) | Inverse cosecant (arccosecant) function | |
sin²(θ) + cos²(θ) = 1 | \sin^2(\theta) + \cos^2(\theta) = 1 | Pythagorean identity | |
1 + tan²(θ) = sec²(θ) | 1 + \tan^2(\theta) = \sec^2(\theta) | Pythagorean identity for tangent and secant | |
1 + cot²(θ) = csc²(θ) | 1 + \cot^2(\theta) = \csc^2(\theta) | Pythagorean identity for cotangent and cosecant | |
sin(2θ) = 2sin(θ)cos(θ) | \sin(2\theta) = 2\sin(\theta)\cos(\theta) | Double angle identity for sine | |
cos(2θ) = cos²(θ) − sin²(θ) | \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) | Double angle identity for cosine | |
tan(2θ) = 2tan(θ) / (1 − tan²(θ)) | \tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)} | Double angle identity for tangent | |
a/sin(A) = b/sin(B) = c/sin(C) | \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} | Law of sines | |
c² = a² + b² − 2abcos(C) | c^2 = a^2 + b^2 - 2ab\cos(C) | Law of cosines | |
θ = s / r | \theta = \frac{s}{r} | Angle in radians as arc length divided by radius | |
s = rθ | s = r\theta | Arc length of a circle | |
(x, y) = (cos(θ), sin(θ)) | (x, y) = (\cos(\theta), \sin(\theta)) | Coordinates on the unit circle | |
tan(θ) = y / x | \tan(\theta) = \frac{y}{x} | Tangent as ratio of ( y ) to ( x ) | |
sinh(x) | \sinh(x) | Hyperbolic sine | |
cosh(x) | \cosh(x) | Hyperbolic cosine | |
tanh(x) | \tanh(x) | Hyperbolic tangent | |
coth(x) | \coth(x) | Hyperbolic cotangent | |
sech(x) | \text{sech}(x) | Hyperbolic secant | |
csch(x) | \text{csch}(x) | Hyperbolic cosecant | |
sinh⁻¹(x) | \sinh^{-1}(x) | Inverse hyperbolic sine | |
cosh⁻¹(x) | \cosh^{-1}(x) | Inverse hyperbolic cosine | |
tanh⁻¹(x) | \tanh^{-1}(x) | Inverse hyperbolic tangent | |
coth⁻¹(x) | \coth^{-1}(x) | Inverse hyperbolic cotangent | |
sech⁻¹(x) | \text{sech}^{-1}(x) | Inverse hyperbolic secant | |
csch⁻¹(x) | \text{csch}^{-1}(x) | Inverse hyperbolic cosecant | |
z = r(cos(θ) + isin(θ)) | z = r(\cos(\theta) + i\sin(\theta)) | Trigonometric form of a complex number | |
eⁱᶿ = cos(θ) + isin(θ) | e^{i\theta} = \cos(\theta) + i\sin(\theta) | Euler's formula | |
zⁿ = rⁿ(cos(nθ) + isin(nθ)) | z^n = r^n(\cos(n\theta) + i\sin(n\theta)) | De Moivre's theorem | |
sin(α + β) = sin(α)cos(β) + cos(α)sin(β) | \sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) | Sine of a sum | |
sin(α − β) = sin(α)cos(β) − cos(α)sin(β) | \sin(\alpha - \beta) = \sin(\alpha)\cos(\beta) - \cos(\alpha)\sin(\beta) | Sine of a difference | |
cos(α + β) = cos(α)cos(β) − sin(α)sin(β) | \cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta) | Cosine of a sum | |
cos(α − β) = cos(α)cos(β) + sin(α)sin(β) | \cos(\alpha - \beta) = \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) | Cosine of a difference | |
tan(α + β) = (tan(α) + tan(β)) / (1 − tan(α)tan(β)) | \tan(\alpha + \beta) = \frac{\tan(\alpha) + \tan(\beta)}{1 - \tan(\alpha)\tan(\beta)} | Tangent of a sum | |
tan(α − β) = (tan(α) − tan(β)) / (1 + tan(α)tan(β)) | \tan(\alpha - \beta) = \frac{\tan(\alpha) - \tan(\beta)}{1 + \tan(\alpha)\tan(\beta)} | Tangent of a difference |