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

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In summary, the conversation discusses a student seeking help in their grade 12 math course and asking for assistance with specific questions. The questions involve solving for x algebraically, finding the cosine of the difference of two angles, and finding the rate of change of the angle of elevation of a balloon from an observer. The student also requests a walkthrough of the steps used to obtain the answers. The responses include specific values for the answers and the use of a TI89 calculator and mathematical formulas to solve the problems.
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recon9
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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!
 
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  • #2
3) I got 0.048rad/sec.

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

1)2.618, 0.524, -3.665, -5.759. :cool:
 
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  • #3
Would you be able to walk me through the steps you took the get those answers? That would be great, thanks!
 
  • #4
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
 

What is the equation to solve for x?

The equation to solve for x is sin2x + 4sinx = cosx + 2 in the interval 0

What is the meaning of "0

The interval 0

How do I solve this equation algebraically?

To solve this equation algebraically, you can use algebraic operations such as combining like terms, factoring, and applying trigonometric identities. You can also use the quadratic formula or solve for x using a graphing calculator.

What are the steps to solve this equation?

The steps to solve this equation are:
1. Combine like terms on both sides of the equation
2. Use trigonometric identities to simplify the equation
3. Isolate the trigonometric function with the variable on one side
4. Apply inverse trigonometric functions to both sides to solve for x
5. Check your solution by plugging it back into the original equation.

What is the solution for x in this equation?

The solution for x in this equation is x = pi/2 or x = 3pi/2. These are the values of x that satisfy the equation in the given interval.

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