Trig. Homegenous Equation (1 Viewer)

[ForbiddenND]

Just a quick question (hopefully).

Question

3tanx - 2cotx + 3 secx = 0

Working

3tanx/1 - 2/tanx + 3/cosx = 0

skip a few steps...

(4sin^2x + 3sinx - 2)/(sinxcosx) = 0

I know you cant get rid of sinxcosx but how do you solve it otherwise. I tried getting rid of sinxcosx but it gets rid of some answers. btw i can do the ones with only 2 trig things (e.g. cos and sin) not with 3. Sorry bout how the equations are showing and skipping steps can't get the dumb (probably me) latex equation thingy to work.

 

[Drongoski]

After some fiddling, you get: ( 5sin^2x +3sin x - 2)/sinxcosx = 0

.: the numerator = 0

i.e. 5sin^2x + 3sin x - 2 = 0

i.e. (5sinx - 2)(sinx + 1) = 0

.: either 5sinx - 2 = 0 ==> sin x = 2/5 (u get the various values of x)

or sin x + 1 = 0 ==> sin x = -1 (u get the various values of x)

In yr answer for values of x, u have to exclude values of x for which sinxcosx = 0 (if any) such as 0 and 90 deg. which would lead to division by zero. That's how u take care of the denominator.

 

[GUSSSSSSSSSSSSS]

yes as drongoski showed:

the denominator has no relevance when you put the equation equal to zero (unless the denominator is undefined)
it is only the numerator that makes a difference
so you solve for the numerator equal to zero

xDD

 

[ForbiddenND]

After some fiddling, you get: ( 5sin^2x +3sin x - 2)/sinxcosx = 0

.: the numerator = 0

i.e. 5sin^2x + 3sin x - 2 = 0

i.e. (5sinx - 2)(sinx + 1) = 0

.: either 5sinx - 2 = 0 ==> sin x = 2/5 (u get the various values of x)

or sin x + 1 = 0 ==> sin x = -1 (u get the various values of x)

In yr answer for values of x, u have to exclude values of x for which sinxcosx = 0 (if any) such as 0 and 90 deg. which would lead to division by zero. That's how u take care of the denominator.

lol thats helpful but can you please explain the last bit dont fully understand it

 

[studentcheese]

What Drongoski means is that you have to work out the values of x that make sinxcosx = 0. If these answers are part of your solution, then you need to get rid of them as x/0 does not exist.

 

[jet]

What Drongoski means is that you have to work out the values of x that make sinxcosx = 0. If these answers are part of your solution, then you need to get rid of them as x/0 does not exist.

It's not that x/0 doesn't exist, it is just that that expression has no mathematical meaning.