☰ Contents · Computing

Mathematical and product functions

Lessons 13–14 · 2 lessons · N. I. Taylaqov (general editor), A. B. Akhmedov, M. D. Pardayeva, A. A. Abdug‘aniyev, U. M. Mirsanov. Informatics and Information Technologies, Grade 10, 1st edition. “Extremum-Press”, Tashkent, 2017
13

Mathematical functions

Textbook: pp. 32–35
GoalWrites mathematical functions (SQRT, ABS, POWER, EXP, LN, COS …) inside one another and builds a table of values of a complex function.
New words
composite function: a function whose argument is another function, such as sin(eˣ) · murakkab funksiyathe number e ≈ 2.71828: the base of natural logarithms, returned by EXP(1) · e soniabsolute value: the distance of a number from zero, ABS(–5) = 5 · mutlaq qiymatradian: the angle unit used by SIN, COS and TAN · radian
Explanation

Most functions in the Math & Trig group take one argument: SQRT(x) is the square root, ABS(x) the absolute value, EXP(x) e to the power x, LN(x) the natural logarithm, and POWER(a, b) is a to the power b (the same as a^b). SIN, COS and TAN expect the angle in radians, RADIANS(d) converts degrees, and PI() gives π ≈ 3.14159. A composite function, for example sin(eˣ), is written =SIN(EXP(A2)): the inner function is calculated first and its result becomes the argument of the outer one. An argument can be a cell, a number or another function. In a table of a function of two variables such as z = sin x + cos y, the x values are in the first row and the y values in the first column, and the formula uses mixed references: =SIN(B$1)+COS($A2). To show results neatly use ROUND or the “Decrease Decimal” button.

Worked examples
At x = 0.5: =SIN(A2) → 0.4794; =EXP(-A2) → 0.6065; =SIN(EXP(-A2)) = sin(0.6065) → 0.5700; =SQRT(1+SIN(A2)) = √1.4794 → 1.2163. All four columns refer to the same x column.
A table of z = sin x + cos y: the x values are in B1:D1 (0; 0.5; 1) and the y values in A2:A4 (0; 0.5; 1). B2 gets =SIN(B$1)+COS($A2) and is copied over the block. In the cell where A3 = 0.5 and C1 = 0.5 meet, the value is sin 0.5 + cos 0.5 ≈ 1.3570; for y = 0 and x = 1 the value is sin 1 + cos 0 ≈ 1.8415.
Class activity

“From the inside out”: the teacher writes a composite function (for example, ln(cos x + 2)); students say which function is calculated first and write the Excel formula in their notebooks (=LN(COS(A2)+2)).

Practice
1
What is the result of =ROUND(SQRT(2),3)?
2
What is =POWER(2,10)?
3
What value does =LN(EXP(2)) give and why?
4
In =SIN(EXP(A2)), which function is calculated first and why?