Solve for x algebraically in the interval 0<x<2pi sin2x + 4sinx = cosx + 2

[recon9]

Hello, I am in grade 12 taking math31 which is pretty much a college course. I am not doing that great in it at the moment and I just found this forum with less than 2 months left in the semester. Anyway, there are a few questions I am stuck on. One of them is:


(note: all of the '<' are less than or equal to)
1. Solve for x algebraically in the interval 0<x<2pi
sin2x + 4sinx = cosx + 2

2. If sin(a)=8/17 , 0<a<pi/2 and tan(b)=7/24 , pi<b<3pi/2, find cos(a-b)

3. A balloon rises at the rate of 3m/s from a point 50m from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 30m above the ground?

Thanks very much!

 

[Ebolamonk3y]

3) I got 0.048rad/sec.

2) 0.9788 = cos (a-b) in radians

1)2.618, 0.524, -3.665, -5.759.

 

[recon9]

Would you be able to walk me through the steps you took the get those answers? That would be great, thanks!

 

[Ebolamonk3y]

1+2 used TI89...

3)

3/4/5 triangle

tan x = y/40 where y is the height, currently 30
take inverse

x = tan^-1(y/40), x=angle

take derivative with respect to t.

dx/dt=1/(40+y^2/40)*dy/dt

dy/dt=3m/s

dx/dt=0.048rad/s