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MTH100 - General Mathematics Assignment No. 2 Solution and Discussion Spring 2014 of VirtualUniversity (VU) Due Date: July 10, 2014
Assignment: # 02 (Spring 2014)
Mth100 (General Mathematics)
Lecture: 19 – 28
Total Marks = 15
Due date: July 10, 2014
Q 1 Write out the expansion of (1 - 2x)7 .
Q 2 Are the lines and parallel, perpendicular, or neither?
Q 3 Find the exact value of Cos 300o .
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Example for Q 1
(1 + 2x)^7 ≈ 1 + 14x + 84x^2 + 280x^3
Letting x = 0.01:
[1 + 2(0.01)]^7 ≈ 1 + 14(0.01) + 84(0.01)^2 + 280(0.01)^3
==> (1.02)^7 ≈ 1.14868
Multiplying both sides by 1.02:
1.02 * (1.02)^7 ≈ (1.02)(1.14868)
==> (1.02)^8 ≈ 1.1716536
by finding the reflex value of 300 Degrees (also known as 60 Degrees), and finding the Cosine of that gives you the answer. Because it is in the 4th Quadrant, the Cosine in positive, so whatever you get from Cos 60 is the actual answer, as in you don't need to make it negative.
360 Degrees is the same as 0 Degrees, in terms of the Unit Circle. To get the Secant, you can do 1 divided by the Cosine of 360.
Note to those above: He asked HOW to do it, not what the answer is. Nonetheless, the first guy is wrong.
Originally, the Cos and Sin function has a period of π, or 360º. So if you add 360º (for degree) or π (for radian) to the angle value, you get the same value of the function.
For example: Sin(30º) = Sin(30º+360º) = Sin(30º-360º) = 0.5
or Sin(-π/6) = sin(-π/6 + π) = -0.5
So cos(300º) = cos(300º - 360º) = cos(-60º) = 0.5