engineering word

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February 2nd 2006, 11:55 AM
mathAna1ys!5

engineering word

The surface of a section of highway makes an angle of A degees with the horizontal. An engineer has found that for a particular section, (d^2-d^2cos^2A)/(d^2-d^2sin^2A) =9/400, where d is the distance along the surface of the road.

a. Make a labeled drawing of the situation.

b. Find a numerical value for one trigonometric function of A.
February 2nd 2006, 01:58 PM
ThePerfectHacker

Quote:

Originally Posted by mathAna1ys!5

The surface of a section of highway makes an angle of A degees with the horizontal. An engineer has found that for a particular section, (d^2-d^2cos^2A)/(d^2-d^2sin^2A) =9/400, where d is the distance along the surface of the road.

a. Make a labeled drawing of the situation.

b. Find a numerical value for one trigonometric function of A.

a)I have no idea how a diagram looks like I am not an engineer, however, I can solve equations.

b) $\frac{d^2-d^2\cos^2A}{d^2-d^2\sin^2A}=(9/400)$ .
Now this problem want to factored thus,

$\frac{d^2(1-\cos^2A)}{d^2(1-\sin^2A)}=9/400$
Thus,
$\frac{1-\cos^2A}{1-\sin^2A}=9/400$ .
By the Pythagorean Identities,
$\frac{\sin^2A}{\cos^2A}=\left(\frac{\sin A}{\cos A}\right)^2=9/400$
By the reciprocal identities,
$(\tan A)^2=\tan^2A=9/400$
Thus,
$\tan=\pm 3/20$

Now just use the one your need (the positive one or negative one) and use the inverse-tan on calculator.
Q.E.D.
February 2nd 2006, 09:30 PM
mathAna1ys!5

diagram

The diagram part of this problem would just be the circle gragh with a right tiangle in it like usual (in the first quadrant i believe) and labeled.