내장 함수와 연산자
GeoGebra Manual
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입력창Input Bar을 사용하여 숫자, 좌표 또는 방정식을 생성하려면 다음과 같은 미리 정의된 함수 및 연산을 사용할 수도 있다. 논리 연산자와 함수는 진릿값Boolean values에 관한 기사에 열거되어 있다.
노트: 미리 정의된 함수는 괄호를 사용하여 입력해야 한다. 함수 이름과 괄호 사이에 공백을 두어서는 안 된다.
연산 / 함수 | 입력 |
---|---|
ℯ (오일러의 수) | Alt + e |
ί (허수단위) | Alt + i |
π | Alt + p 또는 pi |
° (도) | Alt + o 또는 deg |
덧셈 | + |
뺄셈 | - |
곱셈 | * 또는 스페이스 바 |
스칼라 곱 | * 또는 스페이스 바 |
벡터 곱(see Points and Vectors) | ⊗ |
나눗셈 | / |
거듭제곱 | ^ 또는 위첨자 (x^2 or x2 )
|
계승 | ! |
괄호 | ( ) |
x좌표 | x( ) |
y좌표 | y( ) |
z좌표 | z( ) |
편각 (also works for 3D points / vectors) | arg( ) |
켤레 | conjugate( ) |
실수부분Real | real( ) |
허수부분Imaginary | imaginary( ) |
절댓값 | abs( ) |
Altitude angle (for 3D points / vectors) | alt( ) |
부호 | sgn( ) or sign() |
Greatest integer less than or equal | floor( ) |
Least integer greater than or equal | ceil( ) |
Round | round(x) or round(x, y) |
Square root | sqrt( ) |
Cubic root | cbrt( ) |
The nth root of x | nroot(x, n) |
Random number between 0 and 1 | random( ) |
Exponential function | exp( ) or ℯx |
Logarithm (natural, to base e) | ln( ) or log( ) |
Logarithm to base 2 | ld( ) |
Logarithm to base 10 | lg( ) |
Logarithm of x to base b | log(b, x ) |
Cosine | cos( ) |
Sine | sin( ) |
Tangent | tan( ) |
Secant | sec() |
Cosecant | cosec() |
Cotangent | cot() or cotan() |
Arc cosine (answer in radians) | acos( ) or arccos( ) |
Arc cosine (answer in degrees) | acosd( ) |
Arc sine (answer in radians) | asin( ) or arcsin( ) |
Arc sine (answer in degrees) | asind( ) |
Arc tangent (answer in radians, between -π/2 and π/2) | atan( ) or arctan( ) |
Arc tangent (answer in degrees, between -90° and 90°) | atand( ) |
Arc tangent (answer in radians, between -π and π) | atan2(y, x) or arcTan2(y, x) |
Arc tangent (answer in degrees, between -180° and 180°) | atan2d(y, x) |
Hyperbolic cosine | cosh( ) |
Hyperbolic sine | sinh( ) |
Hyperbolic tangent | tanh( ) |
Hyperbolic secant | sech( ) |
Hyperbolic cosecant | cosech( ) |
Hyperbolic cotangent | coth( ) or cotanh() |
Antihyperbolic cosine | acosh( ) or arccosh( ) |
Antihyperbolic sine | asinh( ) or arcsinh( ) |
Antihyperbolic tangent | atanh( ) or arctanh( ) |
Beta function Β(a, b) | beta(a, b) |
Incomplete beta function Β(x;a, b) | beta(a, b, x) |
Incomplete regularized beta function I(x; a, b) | betaRegularized(a, b, x) |
Gamma function Γ(x) | gamma( x) |
(Lower) incomplete gamma function γ(a, x) | gamma(a, x) |
(Lower) incomplete regularized gamma function P(a,x) = γ(a, x) / Γ(a) | gammaRegularized(a, x) |
Gaussian Error Function | erf(x) |
Digamma function | psi(x) |
The Polygamma function is the (m+1)th derivative of the natural logarithm of the Gamma function, gamma(x) (m=0,1) | polygamma(m, x) |
The Sine Integral function | sinIntegral(x) |
The Cosine Integral function | cosIntegral(x) |
The Exponential Integral function | expIntegral(x) |
The Riemann-Zeta function ζ(x) | zeta(x) |
Lambert's W function LambertW(x, branch) | LambertW(x, 0), LambertW(x, -1) |
노트: The x, y, z operators can be used to get corresponding coefficients of a line.
To create numbers, coordinates, or equations using the Input Bar you may also use the following pre-defined functions and operations. Logic operators and functions are listed in article about Boolean values.
노트: The predefined functions need to be entered using parentheses. You must not put a space between the function name and the parentheses.
Operation / Function | Input |
---|---|
ℯ (Euler's number) | Alt + e |
ί (Imaginary unit) | Alt + i |
π | Alt + p or pi |
° (Degree symbol) | Alt + o or deg |
Addition | + |
Subtraction | - |
Multiplication | * or Space key |
Scalar product | * or Space key |
Vector product(see Points and Vectors) | ⊗ |
Division | / |
Exponentiation | ^ or superscript (x^2 or x2 )
|
Factorial | ! |
Parentheses | ( ) |
x-coordinate | x( ) |
y-coordinate | y( ) |
z-coordinate | z( ) |
Argument (also works for 3D points / vectors) | arg( ) |
Conjugate | conjugate( ) |
Real | real( ) |
Imaginary | imaginary( ) |
Absolute value | abs( ) |
Altitude angle (for 3D points / vectors) | alt( ) |
Sign | sgn( ) or sign() |
Greatest integer less than or equal | floor( ) |
Least integer greater than or equal | ceil( ) |
Round | round(x) or round(x, y) |
Square root | sqrt( ) |
Cubic root | cbrt( ) |
The nth root of x | nroot(x, n) |
Random number between 0 and 1 | random( ) |
Exponential function | exp( ) or ℯx |
Logarithm (natural, to base e) | ln( ) or log( ) |
Logarithm to base 2 | ld( ) |
Logarithm to base 10 | lg( ) |
Logarithm of x to base b | log(b, x ) |
Cosine | cos( ) |
Sine | sin( ) |
Tangent | tan( ) |
Secant | sec() |
Cosecant | cosec() |
Cotangent | cot() or cotan() |
Arc cosine (answer in radians) | acos( ) or arccos( ) |
Arc cosine (answer in degrees) | acosd( ) |
Arc sine (answer in radians) | asin( ) or arcsin( ) |
Arc sine (answer in degrees) | asind( ) |
Arc tangent (answer in radians, between -π/2 and π/2) | atan( ) or arctan( ) |
Arc tangent (answer in degrees, between -90° and 90°) | atand( ) |
Arc tangent (answer in radians, between -π and π) | atan2(y, x) or arcTan2(y, x) |
Arc tangent (answer in degrees, between -180° and 180°) | atan2d(y, x) |
Hyperbolic cosine | cosh( ) |
Hyperbolic sine | sinh( ) |
Hyperbolic tangent | tanh( ) |
Hyperbolic secant | sech( ) |
Hyperbolic cosecant | cosech( ) |
Hyperbolic cotangent | coth( ) or cotanh() |
Antihyperbolic cosine | acosh( ) or arccosh( ) |
Antihyperbolic sine | asinh( ) or arcsinh( ) |
Antihyperbolic tangent | atanh( ) or arctanh( ) |
Beta function Β(a, b) | beta(a, b) |
Incomplete beta function Β(x;a, b) | beta(a, b, x) |
Incomplete regularized beta function I(x; a, b) | betaRegularized(a, b, x) |
Gamma function Γ(x) | gamma( x) |
(Lower) incomplete gamma function γ(a, x) | gamma(a, x) |
(Lower) incomplete regularized gamma function P(a,x) = γ(a, x) / Γ(a) | gammaRegularized(a, x) |
Gaussian Error Function | erf(x) |
Digamma function | psi(x) |
The Polygamma function is the (m+1)th derivative of the natural logarithm of the Gamma function, gamma(x) (m=0,1) | polygamma(m, x) |
The Sine Integral function | sinIntegral(x) |
The Cosine Integral function | cosIntegral(x) |
The Exponential Integral function | expIntegral(x) |
The Riemann-Zeta function ζ(x) | zeta(x) |
Lambert's W function LambertW(x, branch) | LambertW(x, 0), LambertW(x, -1) |
노트: The x, y, z operators can be used to get corresponding coefficients of a line.