Basic Engineering Mathematics, Fifth Edition

28 Basic Engineering Mathematics

8. Evaluate cos( 1 .42 rad)


9. Evaluate tan( 5 .673 rad)


10. Evaluate

(sin42. 6 ◦)(tan83. 2 ◦)

cos13. 8 ◦

4.3.6 πandexfunctions

Press Shift and then press the× 10 xfunction key andπ

appears on the screen. Either press Shift and=(or=

andS⇔D) and the value ofπappears in decimal form

as 3.14159265...

Press Shift and then press the ln function key ande

appears on the screen. Enter 1 and then press=and

e^1 =e= 2. 71828182 ...

Now check the followingworked examples involvingπ

andexfunctions.

Problem 18. Evaluate 3.57π

(i) Enter 3.57

(ii) Press Shift and the× 10 xkey and 3. 57 πappears

on the screen.

(iii) Either press Shift and=(or=and S⇔D)

and the value of 3. 57 πappears in decimal as

11. 2154857 ...

Hence, 3. 57 π= 11 .22 correct to 4 significant figures.

Problem 19. Evaluatee^2.^37

(i) Press Shift and then press the ln function key and

eappears on the screen.

(ii) Enter 2.37 ande^2.^37 appears on the screen.

(iii) Press Shiftand=(or=andS⇔D) and the value

ofe^2.^37 appears in decimal as 10.6973922...

Hence,e^2.^37 = 10 .70 correct to 4 significant figures.

Now try the following Practice Exercise

PracticeExercise 18 πandexfunctions

(answers on page 341)

Evaluatethefollowing,each correct to 4 significant

figures.

1. 1.59π 2. 2.7(π−1)
   3. π^2

(√

13 − 1

)

4. 3eπ


5. 8.5e−^2.^5 6. 3e^2.^9 − 1. 6


6. 3 e(^2 π−^1 ) 8. 2πe

π

3

9.

√[

5. 52 π

2 e−^2 ×

√

26. 73

]

10.

√√

√

√

√

⎡

⎣ e

(

2 −

√

3

)

π×

√

8. 57

⎤

⎦

4.4 Evaluation of formulae

The statementy=mx+cis called aformulaforyin

terms ofm,xandc.

y,m,xandcare calledsymbols.

When given values ofm,xandcwe can evaluatey.

There are a large number of formulae used in engineer-

ing and in this section we will insert numbers in place

of symbols to evaluate engineering quantities.

Just four examples of important formulae are:

1. A straight line graph is of the formy=mx+c(see
   Chapter 17).


2. Ohm’s law states thatV=I×R.


3. Velocity is expressed asv=u+at.


4. Force is expressed asF=m×a.
   Here are some practical examples. Check with your
   calculator that you agree with the workingand answers.

Problem 20. In an electrical circuit the voltageV

is given by Ohm’s law, i.e.V=IR. Find, correct to

4 significant figures, the voltage whenI= 5 .36A

andR= 14. 76 

V=IR=( 5. 36 )( 14. 76 )

Hence,voltageV= 79 .11V, correct to 4 significant

figures.

Problem 21. The surface areaAof a hollow cone

is given byA=πrl. Determine, correct to 1

decimal place, the surface area whenr= 3 .0cm

andl= 8 .5cm

A=πrl=π( 3. 0 )( 8. 5 )cm^2

Hence,surface areaA= 80 .1cm^2 , correct to 1 deci-

mal place.