2tan(x)=3sin(x) Solve giving answers within 0 and 360degrees inclusive?

Answer 1

We have
2tanx-3sinx=0
sinx(2secx-3)=0
sinx=0 or cosx=2/3

x=0,360,cos inverse (2/3), 360 - cos inverse (2/3)

Answer 2

2tan(x)=3sin(x)
Here tan(x) cans also be written as sin(x)/cos(x)
Therefore, 2{sin(x)/cos(x)}=3sin(x)
=> 2sin(x)=3sin(x)cos(x)
=> 2sin(x)-3sin(x)cos(x)=0
=> sin(x){2-3cos(x)}=0

Either,
sin (x)=0
=>x= o,360 (for 0 to 360 degree range)

Or,
2-3cos(x)=0
=>3cos(x)=2
=>cos(x)= 2/3
Therefore, x= 48.18968511, 360-48.18968511
=>x= 48.18968511,311.8103149


Therefore,

x=0, 360, 48.18968511, 311.8103149

Answer 3

2tan(x) = 3sin(x), 0 <= x <= 360

First, convert everything to sine and cosine.

2[sin(x)/cos(x)] = 3sin(x)

Multiply both sides by cos(x)

2sin(x) = 3sin(x)cos(x)

Move everything to the left hand side.

2sin(x) - 3sin(x)cos(x) = 0

Factor out sin(x).

sin(x) [2 - 3cos(x)] = 0

Now, equate each factor to 0 to get your solutions.

sin(x) = 0
2 - 3cos(x) = 0

sin(x) = 0 occurs when x = {0, 360}
2 - 3cos(x) = 0 when -3cos(x) = -2, or
cos(x) = (2/3). This occurs at
x = {arccos(2/3), 360 - arccos(2/3)}.

Therefore, your solutions are

x = {0, 360, arccos(2/3), 360 - arccos(2/3)}

arccos(2/3) approximates to 48.19 degrees, so

x = {0, 360, approx. 48.19 , approx. 311.81 }

Answer 4

2.sin x / cos x = 3 sin x
2 sin x = 3 sin x cos x
2 sin x - 3 sinx cosx = 0
sin x (2 - 3 cos x) = 0
sin x = 0, cos x = 2 / 3
x = 0 , 180 , 360 , 48.2 , 311. 8
x = 0 , 48.2 , 180 , 311.8 , 360

Answer 5

4x^2-21x+9=0 multiply(a *c)=(4*9)=36 discover 2 aspects that upload as much as furnish you -21 and multiply to furnish you 36. for this reason -18 and -2 . rewrite the unique equation utilising the hot aspects for b. 4x^2-18x-2x+9=0 ingredient the 1st 2 words then the 2d 2. 2x(2x-9) -a million(2x-9) set 2x-a million=0 and 2x-9=0 and sparkling up for x . 2x=a million 2x=9 x=a million/2 or 0.50 x=9/2 0r 4.50 in case you have problems factoring, you could continuously the quadratic equation. x=-b+-sequare roots of b -4ac /2a

Answer 6

2tan(x)=3sin(x)
2sin(x)/cos(x) = 3sin(x)
2sin(x) = 3sin(x)cos(x)
So 2sin(x) - 3sin(x)cos(x) = 0
So sin(x) ( 2 - 3cos(x) ) = 0
So sin(x) = 0 and cos(x) = 2/3
Therefore x = 0, 180 and 360 degrees and 48.2 and 311.8 (360 - 48.2) degrees.

Answers = 0, 48.2, 180, 311.8, 360 degrees

Answer 7

let t=tan(x/2)
then,tanx=2t/(1-t^2)
and sinx=2t/(1+t^2)
2tan(x)=3sin(x)
2*2t/(1-t^2)=3*2t/(1+t^2)
t(10t^2-2)=0
t=0 or +/-1/sqrt5
x=2arctan(0) or
2arctan(+/-1/sqrt5)
=0,180,360,48.1896851
or (360-48.1896851)
hence,
x=0 deg,180deg,360deg,
48.1896851deg or
311.8103149 deg

[note that
2tan180=3sin180
satisfies the equation
as well]

i hope that this helps

Answer 8

those were both very good explanations but they are missing the midpt. whenever sinx=0 so does tanx=0 and that happens at pi or 180 degrees