Answer:
sin 3 θ = 3 sin θ - 4 sin³θ
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given sin 3 θ
= sin ( 2θ + θ )
apply trigonometric formula
<em> sin ( A + B) = sin A cos B + cos A sin B </em>
<em> sin 2 A = 2 sin A cos B</em>
<em> Cos 2 A = 1 - 2 sin² A </em>
<em> cos ² A - sin ² A = 1</em>
<u><em>Step(ii):</em></u>-
sin 3 θ = sin ( 2θ + θ )
= sin 2θ cosθ + cos2θ sin θ
= 2 sin θ cos θ cos θ +( 1 - 2 sin² θ )sin θ
= 2 sin θ (cos² θ ) + sin θ- 2 sin³ θ
= 2 sin θ ( 1- sin²θ) + sin θ- 2 sin³ θ
= 2 sin θ - 2sin³θ + sin θ- 2 sin³ θ
= 3 sin θ - 4 sin³θ
<u><em>Final answer</em></u> :-
sin 3 θ = 3 sin θ - 4 sin³θ
Answer: 1.44pi
Step-by-step explanation: just plug in 1.2 for r in a=pi(r^2)
Answer: No, the page content of the atlas cannot be replicated on the eReader.
Please check explanations below for solution to question (b)
Step-by-step explanation: The dimensions of the eReader screen is given as 8 inches by 6 inches. In order to move a rectangular shape such as the atlas onto it would require the same measurements or, a measurement that has the same ratio as both the length and width of the screen, but a reduced size.
This brings us to similar shapes. When two shapes (rectangles in this case) are similar, it simply means there is a common ratio between the corresponding sides, that is the length and the width. If rectangle 1 has its side measuring 8 inches, then rectangle 2 would have the corresponding side having a common ratio with that of rectangle 1. This means the corresponding side in rectangle 2 can either be an enlargement (which would mean 8 times a scale of enlargement) or a reduction (which means 8 divided by a scale of reduction).
In the question given, the eReader screen has dimensions of 8 inches by 6 inches. The atlas has dimensions given as 19 inches by 12 inches. By observation we can see that the width of the atlas is times 2 of the screen. The length of the atlas however is not times 2 of the screen. That is;
Ratio = Rectangle 1 : Rectangle 2
Ratio of Width = 6 : 12
Ratio of Width = 1 : 2
Likewise
Ratio of Length = 8 : 19
Ratio of Length ≠ 1: 2
This proves that the atlas cannot be scaled down to fit properly into the screen. A solution to make this possible would be to resize the length of the atlas to become times 2 of the eReader screen. This would result in the atlas having new dimensions given as
Length = 16 inches
Width = 12 inches
This would ensure that both rectangular shapes are similar and the atlas can now be scaled down by a factor of 2 to fit in properly into the eReader screen.