Trigonometry

Constants

Symbol	Value
Degrees	\frac{\pi}{180} = 0.017453292519943295769236907\ldots
Pi	\pi \approx 3.14159265358979323\ldots

Trigonometric Functions

Function	Inverse	Hyperbolic	Area Hyperbolic
Sin	Arcsin	Sinh	Arsinh
Cos	Arccos	Cosh	Arcosh
Tan	Arctan Arctan2	Tanh	Artanh
Cot	Arccot	Coth	Arcoth
Sec	Arcsec	Sech	Arsech
Csc	Arccsc	Csch	Arcsch

Function
FromPolarCoordinates	Converts (\operatorname{radius}, \operatorname{angle}) \longrightarrow (x, y)
ToPolarCoordinates	Converts (x, y) \longrightarrow (\operatorname{radius}, \operatorname{angle})
Hypot	\operatorname{Hypot}(x,y) = \sqrt{x^2+y^2}
Haversine	\operatorname{Haversine}(z) = \sin(\frac{z}{2})^2 The Haversine function was important in navigation because it appears in the haversine formula, which is used to reasonably accurately compute distances on an astronomic spheroid given angular positions (e.g., longitude and latitude).
InverseHaversine	\operatorname{InverseHaversine}(z) = 2 \operatorname{Arcsin}(\sqrt{z})

Trigonometric Simplification

The trigSimplify() method applies the Fu algorithm to simplify trigonometric expressions. This systematic approach uses transformation rules to find simpler equivalent forms.

const expr = ce.parse("\\sin^2(x) + \\cos^2(x)");
expr.trigSimplify();  // Returns: 1

const expr2 = ce.parse("2\\sin(x)\\cos(x)");
expr2.trigSimplify(); // Returns: sin(2x)

Alternatively, use the strategy option with simplify():

expr.simplify({ strategy: 'fu' });

Supported Identities

The Fu algorithm recognizes and applies:

• Pythagorean identities: sin²(x) + cos²(x) = 1, 1 + tan²(x) = sec²(x)
• Reciprocal identities: sec(x) = 1/cos(x), csc(x) = 1/sin(x)
• Double angle formulas: sin(2x) = 2sin(x)cos(x), cos(2x) = cos²(x) - sin²(x)
• Product-to-sum: sin(x)cos(y) = ½[sin(x+y) + sin(x-y)]
• Sum-to-product: sin(x) + sin(y) = 2sin((x+y)/2)cos((x-y)/2)
• Morrie's law: Products of cosines with doubled angles

Read more about Simplification