Numerical expressions are formed from numbers, signs of arithmetic actions and brackets. If at such expression there are variables, it will be called algebraic. Expression in which the variable contains under signs of trigonometrical functions is trigonometrical. Tasks on determination of values of numerical, trigonometrical, algebraic expressions often meet in a school course of mathematics.
1. To find value of numerical expression, define an operations procedure in the set example. For convenience designate it by a pencil over the corresponding signs. Perform all specified operations in a certain order: actions in brackets, exponentiation, multiplication, division, addition, subtraction. The received number will also be value of numerical expression.
2. Example. Find value of expression (34∙10+ (489–296) ∙8): 4–410. Define an operations procedure. Perform the first operation in internal brackets 489–296=193. Then, increase 193∙8=1544 and 34∙10=340. Following action: 340+1544=1884. Further execute division 1884:4=461 and then subtraction 461–410=60. You found value of this expression.
3. To find value of trigonometrical expression at the known coal α, previously formulas. Calculate preset values of trigonometrical functions, set up them as an example. Perform operations.
4. Example. Find value of expression 2sin 30º ∙ cos 30º ∙ tg 30º ∙ ctg 30º. Simplify this expression. For this purpose use a formula tg α ∙ ctg α=1. Receive: 2sin 30º ∙ cos 30º ∙ 1=2sin 30º ∙ cos 30º. It is known that sin 30º=1/2 and cos 30º= √ 3/2. Therefore, 2sin 30º ∙ cos 30º=2∙1/2 ∙√ 3/2= √ 3/2. You found value of this expression.
5. The value of algebraic expression depends on value of a variable. To find value of algebraic expression at the set variables, simplify expression. Substitute certain values instead of variables. Perform necessary operations. As a result you receive number which will be value of algebraic expression at the set variables.
6. Example. Find value of expression of 7 (a+y) –3 (2a+3y) at a=21 and y=10. Simplify this expression, receive: a–2y. Substitute the corresponding values of variables and calculate: a–2y=21–2∙10=1. It is also value of expression of 7 (a+y) –3 (2a+3y) at a=21 and y=10.