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Cos

Cos[z]
gives the cosine of z.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The argument of Cos is assumed to be in radians. (Multiply by Degree to convert from degrees.)  »
  • Cos is automatically evaluated when its argument is a simple rational multiple of Pi; for more complicated rational multiples, FunctionExpand can sometimes be used.  »
  • For certain special arguments, Cos automatically evaluates to exact values.
  • Cos can be evaluated to arbitrary numerical precision.
  • Cos automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (4)
The argument is given in radians:
Use Degree to specify an argument in degrees:
The argument is given in radians:
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Use Degree to specify an argument in degrees:
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In[1]:=
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Scope   (11)
Evaluate numerically:
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Cos threads element-wise over lists and matrices:
Simple exact values are generated automatically:
More complicated cases require explicit use of FunctionExpand:
Convert multiple-angle expressions:
Convert sums of trigonometric functions to products:
Expand assuming real variables:
Convert to complex exponentials:
TraditionalForm formatting:
Generalizations & Extensions   (4)
Cos can deal with real-valued intervals:
Infinite arguments give symbolic results:
Cos can be applied to power series:
Cos threads element-wise over sparse arrays as well as lists:
Applications   (11)
Draw a circle:
Lissajous figure:
Equiangular (logarithmic) spiral:
Circular motion:
Solve an equation for harmonic motion:
Rotation matrix:
Apply to a horizontally aligned vector:
Plot a sphere:
Plot a torus:
2D waves:
Triple-periodic surface:
Approximate the almost nowhere differentiable Riemann-Weierstrass function:
Properties & Relations   (10)
Basic parity and periodicity properties of the cosine function get automatically applied:
Complicated expressions containing trigonometric functions do not simplify automatically:
Compose with inverse functions:
Solve a trigonometric equation:
Numerically find a root of a transcendental equation:
Reduce a trigonometric equation:
Integrals:
Fourier transform:
Cos appears in special cases of many mathematical functions:
Cos is a numeric function:
Possible Issues   (5)
Machine-precision input is insufficient to give a correct answer:
With exact input, the answer is correct:
A larger setting for $MaxExtraPrecision can be needed:
Machine-number inputs can give high-precision results:
Continuous functions involving Cos[x] can give discontinuous indefinite integrals:
In traditional form parentheses are needed around the argument:
Neat Examples   (5)
Chladni figure:
Plot Cos at integer points:
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