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# How do I solve: 3cosx+4sinx+3=0 watch

1. How do I solve: 3cosx+4sinx+3=0 Where x is between 0 & 360

I'm not sure how to begin !

Thanks,
Ross
2. try expressing it in the form of Rcos(x+/-a) or Rsin(x+/-a)
3. I think iteration is the only way to solve this kind of question. I'm in AS so I don't know that how iteration is applied, but you may search on google for it.
4. ive just finished this chapter in C2 last week and i think it wud be helpful if u used the formula: sinx/cosx = tanx

so it would be 4/3tanx + 3=0
then make tanx the subject and find tan-1 in ur calculator and then u can use the quadrant rule or the graph to help u find the angles
5. (Original post by cj_134)
try expressing it in the form of Rcos(x+/-a) or Rsin(x+/-a)
Zishi gave you the correct answer for people with C3 knowledge.

Another approach for those with a little more knowledge is to use a half tangent substitution.
6. (Original post by Rossblunsden)
How do I solve: 3cosx+4sinx+3=0 Where x is between 0 & 360

I'm not sure how to begin !

Thanks,
Ross
THere is more way to solve this equation.
For example you can solve it graphically.

It seems most simple for me to use trigonometric identity of

and from this change sinx with

And arrange the equation

Take square both side and solve for cosx

Another method is the use of another tigonometric identity.

We don't know sinA and cosA but we know from the equation that
the ratio of them is 3/4 that is

Taking square both equation and adding them

So sinA=3/5 cosA=4/5 and tanA=3/4 -->A
Divide the original equation by 5 and substitute

THe third method maybe that arranging the equation you use the identity of
and

THe equation

Arranging to 0 and taking out sinx/2 as factor it gives the solutions

The 4th method would be writing up sine and cosine with t=tanx/2

dividing by cosine squared

So

that is

Substituting them to the original equation we get a quadratic for t.

The fifth method maybe if use the identity of

Arranging the equation and dividing by cosx (cosx=0 would be examined as solution)

So we've got a quadratic equation for tanx

Another method would be using complex valued, so
exponential functions.

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