Hi,
For these: http://imgur.com/a/x7Y8L
Q14a) I'm confused in some parts of the book's answer. In their diagram why are they measuring alpha between the line and the y-axis, don't we usually measure between the x-axis? I did the latter which got me the reciprocal of what they had for tan(alpha).
Also, when they write tan(alpha) = at/bt, why do you/are allowed to omit the minus sign? I left the minus sign in there but ended up with an answer with both components being positive which doesn't make sense here.
Q16c) I have x = t^2 -5t -2 and y = 2 which are correct. I was stuck here but the answer concluded that y=2 was the Cartesian equation. How and why did they do this?
Hi,
Q14a) In the diagram, they measure alpha between the line and the y-axis because it specifies that alpha is given by Na
oW, which is a compass bearing. How this compass bearings is N tells you to face North, and then turn alpha
o towards West, where North represents the positive direction of the y-axis and West represents the negative direction of the x-axis.
When they write tan(alpha) = at/bt, they omit the minus sign because when working with triangles and trigonometry, the lengths of the sides must be positive for the triangle to exist. To illustrate, when you draw a triangle to represent cos(2pi/3) = -1/2, you still draw the lengths of the sides as 1 and 2, not -1 and 2.
Q16c) The reason the answer concluded y=2 is because no matter what x equals, y will still equal 2. Normally you would be able to express t in terms of x and then substitute but in this case y(t) has no t term to allow such a substitution. That's why the conclusion is y=2. However, it should be noted that y=2 only exists for x greater or equal to -33/4, because the range of x(t) is [-33/4,infinity], which means x only has values for this range.
Hope this helps!!!