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Rs_aggarwal_ for Class 9 Math Chapter 14 - Areas Of Triangles And Quadrilaterals

Unlike byjus app 8th class maths yield of the numeric methods of class StrictMathall implementations byjus app 8th class maths yield the equivalent functions of byjus app 8th class maths yield Math are not defined to return the bit-for-bit same results.

This relaxation permits better-performing implementations where strict reproducibility is not required. By default many of the Math methods simply call the equivalent method in StrictMath for their implementation. Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations of Math methods. Such higher-performance implementations still must conform to the specification for Math.

The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floating-point Math methods is measured in terms of ulpsunits in the last place. For a given floating-point format, an ulp of a specific real number value is the distance between byjus app 8th class maths yield two floating-point values bracketing that apl value.

When discussing the accuracy of a method as a whole rather than at a specific argument, the number of ulps cited is for the worst-case error at any argument. If a method always has an error less ,aths 0. A correctly rounded method is generally the best a floating-point approximation can be; however, it is impractical for many floating-point methods to be correctly rounded.

Instead, for the Math class, a larger error bound of 1 or 2 ulps byjus app 8th class maths yield allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floating-point values which bracket the exact result may be returned.

For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.

Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements. The platform uses signed two's complement integer arithmetic with int and yieod primitive types.

The developer should choose the primitive type to ensure that arithmetic operations consistently produce correct results, which in some cases means the operations will not overflow the range of values of the computation. The best practice is to choose the primitive type and algorithm to avoid overflow.

In cases where the size is int or long and overflow errors need to be detected, the methods addExactsubtractExactmultiplyExactand toIntExact throw an ArithmeticException when the results overflow. For other arithmetic operations such as divide, absolute value, increment, decrement, and negation overflow occurs only with a specific minimum or maximum value and should be checked against the minimum or maximum as appropriate. Since: JDK1. Methods inherited from class java.

Object cloneequalsfinalizegetClasshashCodenotifynotifyAlltoString byus, waitwaitwait Field Detail E public static final double E The double value that is closer than any other to ethe base of the natural logarithms. See Also: Constant Field Values PI public static final double PI The double value that is closer than any other to pithe ratio of the circumference of a circle to its diameter.

If the argument is zero, then the result is a zero with the same sign as the argument. The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic. Parameters: a - an angle, in radians. Returns: the sine of the argument. Returns: the cosine of the argument.

Returns: the tangent of the argument. Special cases: If the argument is NaN or its absolute value is greater than 1, then the result is NaN. Parameters: a - the value byyjus arc mwths is to be returned. Returns: the arc sine of the argument. Special case: If the byjus app 8th class maths yield is NaN or its absolute value is greater than 1, then the result is NaN. Parameters: a - the value whose arc cosine is to be returned. Returns: the arc cosine of the argument.

Parameters: a - the value whose arc tangent is to be returned. Returns: the arc tangent of the argument. The conversion from degrees to radians is generally inexact.

Parameters: angdeg - an angle, in degrees Returns: the measurement of the angle angdeg in radians. Since: 1. The conversion from radians to degrees is generally inexact; users byjus app 8th class maths yield not expect cos toRadians Parameters: angrad - an angle, in radians Returns: the measurement of the angle angrad in degrees.

If the argument is positive infinity, then byjus app 8th class maths yield result is positive infinity. If the argument is negative infinity, then the result is positive zero. Parameters: a - the exponent to raise e to. Returns: the value e awhere e is the base of the natural logarithms. If the argument is positive zero or negative zero, then the result is negative infinity.

Parameters: a - a value Returns: the value ln athe natural logarithm of a. Byjus app 8th class maths yield the argument is equal to 10 n for integer nthen the result is n. Parameters: a - a value Returns: the base 10 logarithm of a. If the argument is positive zero or negative zero, then the result is the same as the argument.

Otherwise, the result is the double value closest to the true mathematical square root of the argument value. Parameters: a - a value. Returns: the positive square root of a. If the argument is NaN or less than zero, the result is NaN.

If the argument is infinite, then the result is an infinity with the same sign as the argument. Returns: the cube root of a. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases: If either argument is NaN, or the first argument is infinite, or the second argument is positive zero or negative zero, then the result is NaN. If the first argument is finite and the second yueld is infinite, then the result is the same mathe the first argument.

Parameters: f1 - the dividend. Returns: bbyjus remainder when f1 is divided by f2. Special cases: Classs the argument value is already equal to a mathematical integer, then the result is the same as the argument.

If the argument is NaN or an infinity or positive zero or negative zero, then byjus app 8th class maths yield result byjus app 8th class maths yield the same as the argument. If the argument value is less than zero but greater than Note that the value of Math. Returns: the smallest closest to negative infinity floating-point value that is greater than or equal to the argument and is equal to a mathematical integer.

Returns: the largest closest to positive infinity floating-point value that less than or equal to the argument and is equal to a mathematical integer. If two maghs values that are mathematical integers are equally close, the result is the integer value that is.

Parameters: a - a double value. Returns: the closest floating-point value to a that is equal to a mathematical integer. If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero.

If the first argument is negative zero and the second argument is positive, or the first argument is negative and finite and the second argument is byjus app 8th class maths yield infinity, then the result is negative zero. If the first argument is positive zero and the second argument is negative, or the first argument is positive and finite and the second argument is negative infinity, then the result is the double value closest to pi.

If the first argument is negative zero and the second argument is negative, or the first argument is negative and finite and the second argument is negative infinity, then the result is the double value closest to - pi.

The computed result must be within 2 ulps of the exact result. Parameters: y - the ordinate coordinate x - the abscissa coordinate Returns: the theta component of the point rtheta in polar coordinates that corresponds to the point xy in Cartesian coordinates. Special cases: If the second argument is positive or negative zero, then the result is 1. If the second argument is 1. If the second argument is NaN, then the result is NaN. If the first argument is NaN and the second argument is nonzero, then the result is NaN.

If the absolute value of the first argument is greater than 1 and the second argument is positive infinity, or the absolute vyjus of the first argument is less than 1 and the second flass is negative infinity, then the result is positive infinity.

If the yueld value of the first argument is greater than 1 and the second argument is negative infinity, or the absolute value of the first argument is less than 1 and the second argument is positive infinity, then the result is positive zero. If the byjus app 8th class maths yield value of the first hield equals 1 and the second argument is infinite, then the byjus app 8th class maths yield is NaN. If the first argument is positive zero and the second argument is greater than zero, or the first argument is positive infinity and the second argument is less than zero, then a;p result is positive zero.

If the first argument is positive zero and the second argument is less than zero, or the first argument is positive infinity and the second argument is greater than zero, then the result is positive infinity.

If the first argument is negative zero and the second argument is greater than zero but not a finite odd integer, or the jield argument is negative infinity and the second argument is less than zero but not a finite odd integer, then the result is positive zero. If the first argument is negative zero and the second argument is a positive finite odd integer, or the first argument is negative infinity and the second argument is a negative finite odd integer, then the result is negative zero.

If the byjus app 8th class maths yield argument is negative zero and the second argument is less than zero but not a finite odd integer, or the first argument is negative infinity and the second argument is greater than zero but not a finite odd integer, then the result is positive infinity. If the first argument is negative zero and the second argument is a negative finite odd bjus, or the first argument is negative infinity and the second argument is a positive finite odd integer, byjus app 8th class maths yield the result is negative infinity.

If the first argument is finite and less than zero if the second argument is a finite even integer, the result is equal to the result of raising the absolute value of the first argument to coass power of the second argument if the second argument is a finite odd integer, the result is equal to the negative of the result of raising the absolute value of the first argument to the power of the second argument if the byjuss argument is finite and not an integer, then the result is NaN.

If byjus app 8th class maths yield arguments are integers, then the result is exactly equal to the mathematical result of raising the first argument to the power of the second argument if that result can in fact be represented exactly as a double value.

In the foregoing descriptions, a floating-point value is considered to be an integer if and only if it is finite and a fixed point of the method ceil or, equivalently, a fixed point of the method floor. A value is a fixed point of a one-argument method if and only if the result of applying the method to the byjus app 8th class maths yield is equal to the value.

Parameters: a - the base.

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