ASSIGNMENT

Assignment



Assignment

Introduction

The paper attempts to present the solution to some of the mathematical questions. It focuses on various aspects of the mathematical calculations including simple algebra, graphical representation of trigonometry, simple trigonometry as well as the calculations of area and volume of different objects.

Discussion

The tasks are computed as below:

Task 1: Using the laws of indices simplify and where possible solve the following:

X5 x X3 - X1 x X2 - X

X8 - X3 - X

a4 / (a

a4 / a0.5

a(4 - 0.5)

a3.5

2(a7 (2(41) x 44 +30 x 32

40.5 x 44 + 30 x 32

44.5 + 322(49 + 32

2((262144) + 9

512 + 9

521

Task 2: Using the laws of logarithm simplify and where possible solve the following:

4log x - log x3 = log y-0.5 + 2log y

Task 6: Plot Graphs:

The relevant table for this question is as below;

Set

1

2

3

4

5

6

7

8

9

10

n

2

3

4

1

7

8

2.5

5

4..5

3.5

The allocated set for me is the set 2, which indicates the value 3 for 'n' for a range of 0 to 360 degrees. The table and graphs of y = cos (3 x ?°) and y = sin (3 x ?°) over range ? = 0° to 360° are provided below:

The calculation of Cos (3 x ?°) and Sin (3 x ?°) have been rounded to 3 digits.

Degrees

1

10

20

50

90

150

180

220

270

320

360

Cos (3 x ?°)

0.999

0.866

0.5

-0.866

0

0

-1

0.5

0

-0.5

1

Sin (3 x ?°)

0.052

0.5

0.866

0.5

-1

1

0

-0.866

1

-0.866

0

Both the functions have the maximum and minimum values of 1 and -1.

For Cos, the maximum values occur at 360°, 720° and 1080° while the minimum value occurs at 180°, 540° and 900°. For Sin, the maximum value occurs at 90°, 450° and 810° while the minimum value occurs at 270°, 630° and 990°.

For both Sin and Cos functions, the separation gap between the maximum values is of 360°.

For Cos the value is -0.866025404 while for Sin it is 0.5.

The table using which the graph of Tan was plotted ...