trigonometry and triangle questions. (1 Viewer)

girlworld_club

Member
I am having trouble answer the following questions: if anyone can help me that would be greatly appreciated.

http://i41.tinypic.com/24zk3ew.png (Q14 only)

http://i41.tinypic.com/2d2bu40.png (question 12)

the book has answers, but no worked solutions. If anyone wants to revise by working it out it would really help me understand because it is usually my technique which get's the wrong answer.

Agaian, thank you so much!!!

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HSC2014

Member
a. We can see that OM is a perpendicular bisector of QR (radius to midpoint of chord is perpendicular)
From here, angle QOM = theta...
b. Area of PQR = 1/2 QR (PM) [1/2 b.h]...
c. Differentiate the above equation with respect to theta...

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HeroicPandas

Heroic!
Q12)
a) T = 2pi/n (and n= pi/8), so the period of this particle is 16seconds
b) Max and min displacement, means max and min values of 'x'. By looking at the graph, we can see that the max and min values for displacement is x = 3 and x = -3 respectively (or if u wanna do it algebraically, find the range of x)
$\bg_white -1 \leq sin\left ( \frac{\pi}{8}x \right ) \leq 1 \\ \\ \therefore -3\leq 3sin\left ( \frac{\pi}{8}x \right ) \leq 3 \\ \\ \therefore -3\leq x\leq 3$
Lower bound of inequality = minimum displacement (-3)
Upper bound of inequality = maximum displacement (+3)
c) Observe graph at the stationary points and identify the t-values that corresponds to it. Or u can do it algebraically, by letting x = -3 and x = 3, solve trig equation and take the smallest times (which are the earliest)
d) Particle's initial position is x = 0, solet x = 0 and solve trig equation to find the times (or observe graph and identify the times when the graph cuts the t-axis as this is when its position is at x = 0)
e) Let t = 20, find x. Or observe graph when t= 20, u notice x = 3 (which is on the POSITIVE side of the origin)
f) From t = 0 to t= 4, particle has travelled 3 units. From t = 4 to t = 8, particle has travelled 3 units etc etc. (or u can do from t = 0 to t = 8 it travels 6 units then continue)

OR, find the velocity equation by differentiating the displacement equation with respect to 't' and then integrating back from t = 0 to t = 16

$\bg_white Distance traveled = \int_0^{16} \frac{3\pi}{8}cos\left ( \frac{3\pi t}{8} \right )dt$

Because: $\bg_white x = \int_{t_1}^{t_2}vdt$

HeroicPandas

Heroic!
I am not sure about part (a) (maybe minimum displacement is x = 0)

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