Help SMR with math homework!

[Govind]

Derivatives of Trigonometric functions:
1. An observer on the ground sights an approaching plane flying at a constant speed and at an altitude of 20000 ft. From the observers point of view, the plane's angle of elevation is increasing at a rate of 0.5 degrees/second when the angle is 60 degrees. Determine the speed of the plane.

2. The graph of y = x-2cos(x) has two tangent lines each having a slope of 1. Determine the equations of these two lines.

Please go step-by-step/show work. Thanks!

 

[Ahtoemick.]

The second seems pretty simple and I can probably help you with it, but I'm about to pop out now (to a maths class funnily enough >.>) so hit me up on IRC sometime in the future if you still need help. I'll come back to this thread and do a step by step anyhow but it's always good to explain in realtime.

I wont be able to help you with the first as it's not a subject we cover in my course.

 

[Shredderbeam]

Derivatives of Trigonometric functions:
1. An observer on the ground sights an approaching plane flying at a constant speed and at an altitude of 20000 ft. From the observers point of view, the plane's angle of elevation is increasing at a rate of 0.5 degrees/second when the angle is 60 degrees. Determine the speed of the plane.

2. The graph of y = x-2cos(x) has two tangent lines each having a slope of 1. Determine the equations of these two lines.

Please go step-by-step/show work. Thanks!

Ok, well for the first problem, we basically have a right triangle - ABC.

<A is 60 degrees, this is given to us.
<B is 90 degrees, as it's a right triangle.
<C is 30 degrees, as all angles must add up to 180.

We know that the altitude is 20,000 , so line C is 20,000 (sides of the triangle will be named for the angle that they are opposite).

Law of Sines = (sin A)/A = (sin B)/B, so:

(sin 30)/20,000 = (sin 90)/ B

0.000025 = 1/B

0.000025B = 1

40,000 = B

So now that we have two sides, we can use the Pythagorean Theorem to figure out side A:

A^2 + 400,000,000 = 1,600,000,000

A^2 = 1,200,000,000

A = 34,641.0162

If we figure that <A is increasing by half a degree, then we divide 34,641.0162 by 120 (the number of half-degrees in <A), and we get 288.675135 feet per second.

I'd try number two, but I'm very tired tonight. Perhaps tomorrow.

 

[Shin]

2. The graph of y = x-2cos(x) has two tangent lines each having a slope of 1. Determine the equations of these two lines.

I used my graphing calculator. When I saw the graph, it was obvious that it had Y-Intercepts at 2 and -2, as by which the equation tells you.

Therefore, your two equations are:

• x+2
• x-2

Such an easy problem. Just graph it. Lmao.
-I'm lol'ing mostly at Darren, because it took me 5 seconds.

 

[Govind]

Thank you Darren & unb4nn3d.