EVOLVING ENGLISH IN STUDY OF MATHEMATICS

Logarithms usually find out the exponential problem if known main numbers and product of exponential. There are several properties of logarithms. First, logarithms based b of x equals to y, b as based. To find out the value of x, can solve by b power y, y as the power. For example, logarithms based ten of one hundred equals to x. If we use the first properties of logarithms, so ten as based power x equals to one hundred. So that, we can find the value of x. the value of x is the positive numbers. In the same ways, if in fraction form, so the value of x is negative numbers. Second, logarithms based e of x equals to ln e, e as irrational numbers. ln e usually called by natural logarithms. Except that, there are three properties again about logarithms especially for characteristics in calculate about logarithms. First, logarithms based b of M times N, so the solution is logarithms based b of M plus logarithms based b of N. So that, in logarithms multiplication form can change to addition form. The same way, if it division form can change to subtraction form. So, logarithms based b of M divided by N equals to logarithms based b of M minus logarithms based b of N. And the last, logarithms based b of x power n. So, the solution is n as power can change as multiple numbers. So that, it equals to n times logarithms based b of x.
In common factors and grouping, we will recognize about product and factors. For example, three times five equals to fifteen. Three and five are factors, but fifteen is product of factors. Factoring means to have all factors are prime numbers. Usually to find The Greatest Common Factor (GCF), we have given two numbers. There are several steps that have to do. For the first step, find out the factors. The factors consist of prime numbers. After that, make it to be a simple form by use exponent. For example, the factors of forty five are five times three times three. If we write like that, it can so long. So, we can make it to be simple form. It will be three square. Then, find out the same factors from two numbers. And to solve it, look for the same factors that have the smallest exponent. After get it, multiply the factors. So, the product of multiply of factors is the greatest common factors.
Trig function usually related with triangle especially right triangle and angle that available in triangle. To solving problem in trig function, you need to know the value of sides in triangle to find measure of an angle. There are six basic in trig function. They are sine, cosine, tangent, cosecant, secant, and cotangent. The trig function defined by sides of a triangle and angle being measure. If there is a right triangle and it has an angle, example theta as an angle in a right triangle, so the sides in front of theta called by OPP (side opposite theta). And the sides beside of theta called by ADJ (side adjacent to theta). And the sides called by HYP (hypotenuse of theta). So, the six trig functions for the theta for sine of theta equals to OPP over HYP, for cosine of theta equals to ADJ over HYP, and for tangent of theta equals to OPP over ADJ. for cosecant, secant, and cotangent of theta, we can find by folding over from sine, cosine, and tangent. Cosecant is folding over of sine, so cosecant of theta equals to HYP over OPP. Secant is folding over of cosine, so secant of theta equals to HYP over ADJ. Then cotangent is folding over of tangent, so cotangent of theta equals to ADJ over OPP. For make us easy to remember it, we can called the short name is SOH CAH TOA.
One way to find factors polynomial is use algebraic long division. To find out factoring polynomials, we can use arranged division. We can find out the factors of polynomial. We can use algebraic long division to calculate polynomials that have more than one degree equation. So, we can solve polynomials that have two, three, etc degree by use algebraic long division. For example, x cube minus seven x minus six divided by x minus three. We can solve this problem by use arranged division have learned in elementary school. In x cube minus seven x minus six, the second degree term no has value or zero. X cube divided by x minus three. The product is x square. Then x square multiply x minus three, so x cube minus three x square. Do the same step until get zero. Here x minus three as the factors. But it’s only one of them. For third degree equation have three roots. The degree of polynomial equation always limits the number of roots. For second degree equation always have two roots. For fourth degree equation have four or fewer roots. To solve long division for a third order polynomials are find a partial quotient of x square by dividing x into x cube to get x square, then multiply x square by the divisor and subtract the product from the dividend. Repeat the process until reach a remainder. Polynomials consist of odd and even degrees.
A function is an algebraic statement that provides a link between two or more variables. Use to find the value of one variable if you know the values of the others. For example, y equals to two x. If you know x, you can find y. So that, to solve this problem, we consider that the value of x is a numbers. Such as, if the value of x is five, so y equals to two times five. It’s ten. The value of y is ten. Function is relation in which each element of one set is paired with one and only one, element of the second set. There are two kinds of relations, equations and inequalities. For example, one plus five equals to six. It’s an equation. But it’s different for inequalities. For example, eight is more than five. Function of x usually called by f(x), f of x. f(x) equals to y. for example, y equals to three x plus four. Three x plus four called by function of x. So, y equals to f(x) equals to three x plus four. It is standard form of function of x. f(x) =3x+4. Many alphabets that can use for sign a function. If given an equation g(x) = x^2-3x+2 and x equals to five. So we can substitute the value of x have known into an equation. We will find out the product or the value of function.
Parallelogram has four sides. But it has special thing. If a quadrilateral is parallelogram, then opposite sides are parallel. If side AB is parallel to side CD and side AC is parallel to side BC. So, it’s called by parallelogram. (AB ) ̅ || (DC) ̅ , (AD) ̅ || (BC) ̅.