General Determine 2sinx + cosecx - 3 = 0

In summary, the general solution of the equation 2sinx + cosecx - 3 = 0 can be found by setting 2sinx + cosecx = 0 and solving for x, which results in the solutions of x = 30 degrees and x = 90 degrees. Substituting these values back into the original equation confirms that they satisfy the equation.
  • #1
DERRAN
34
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Homework Statement


determine the general solution of the equation:
2sinx +cosecx -3 = 0


Homework Equations





The Attempt at a Solution


Dont know what to do need help please.
 
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  • #2
What is cosecx equal to?

When you find that, try multiplying by sinx throughout and see what happens from there.
 
  • #3
Okay I mapped sinx and got:
2sin^{2}x-3sinx+sinx=0
(2sinx-1)(sinx-1)=0
2sinx=1 or sinx=1
sinx=1/2

Is this correct?
 
  • #4
You should learn to check your answers. Let's test it, if sinx=1/2 then the equation becomes:

2*1/4-3*1/2+1/2=-1/2!=0

So no it is not right.
 
Last edited:
  • #5
But x=30 or x=90
then,
substitute in the original equation of 2sinx + cosecx and you get the R.T.P answer of 3.
 
  • #6
Okay I mapped sinx and got:
2sin^{2}x-3sinx+sinx=0
(2sinx-1)(sinx-1)=0
2sinx=1 or sinx=1
sinx=1/2p

I see what happened now. You meant to write 2sin^{2}x-3sinx+1=0 instead of 2sin^{2}x-3sinx+sinx=0. I checked your answer continuing from your first equation, which is wrong. All other steps are correct and your answers satisfy the original equation.
 
  • #7
Thanks for helping
 
  • #8
DERRAN said:
Thanks for helping

Just remember that you were asked to give the general solution and not just solve in a given range.
 

FAQ: General Determine 2sinx + cosecx - 3 = 0

What is the equation "2sinx + cosecx - 3 = 0" representing?

The equation "2sinx + cosecx - 3 = 0" is a general equation that represents a relationship between the sine and cosecant functions with a constant value of -3.

What is the general solution to "2sinx + cosecx - 3 = 0"?

The general solution to "2sinx + cosecx - 3 = 0" is a set of values for x that satisfy the equation. In this case, the general solution is x = 2nπ ± π/6, where n is any integer.

How do you solve "2sinx + cosecx - 3 = 0" algebraically?

To solve "2sinx + cosecx - 3 = 0" algebraically, you can use trigonometric identities to rewrite the equation as (2sinx - 3)(cosecx - 1) = 0. From here, you can solve for each factor separately to find the general solution.

What are the possible values for x in "2sinx + cosecx - 3 = 0"?

The possible values for x in "2sinx + cosecx - 3 = 0" are all real numbers that satisfy the equation. However, since the cosecant function is undefined at x = 0, the solutions must exclude x = 0.

How does the graph of "2sinx + cosecx - 3 = 0" look like?

The graph of "2sinx + cosecx - 3 = 0" is a combination of the sine and cosecant functions, resulting in a series of curves that intersect at certain points. The graph is symmetrical about the line x = π/2 and has asymptotes at x = 0 and x = π.

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