+0

# solve cot x + 6 sin x - 2 cos x =3

0
283
2

solve cot x + 6 sin x - 2 cos x =3

Guest Jun 27, 2017
Sort:

#1
+79894
+5

cot x + 6 sin x - 2 cos x =3     we can write

cosx / sinx  +  6sin x - 2 cosx  = 3       multiply through by sin x

cos x  +  6 sin^2x  -  2cosx sin x  =  3sin x

cos x + 6sin^2x  - 2sin cos x  - 3sin x  = 0         we can factor this as

( 3sinx  - cosx) (2sinx  - 1) = 0      set each factor to 0  and solve

3sinx  - cos x  = 0

3sin x  = cos x

3sinx / cos x  =  1

3 tan x  =  1

tan x  = 1/3

arctan (1/3)  ≈  18.435°  + 180°n    where  n is an intreger

For the other factor we have that

2sinx - 1  = 0

2sin x  = 1

sin x  =  1/2

arcsin (1/2)    and this happens at  30° + 360°n    and at  150° + 360°n

And again, n is an integer

Here's ther graph : https://www.desmos.com/calculator/eiai1cs0i1

CPhill  Jun 27, 2017
#2
+5573
+4

Nice CPhill  !! This was harder than it first looks, for me at least !  Here is just the factoring part. I did it at first just to see it for myself, and then I figured it couldn't hurt to post it.

cos x  +  6 sin2x  -  2 sin x cos x  -  3 sin x   =   0        Rearrange.

6 sin2x  -  3 sin x  +  cos x  -  2 sin x cos x   =  0         Factor out  3 sin x  from the first two terms and

factor out  -cos x  from the last two terms.

3 sin x (2 sin x - 1)  -  cos x (-1 + 2 sin x)  =  0             Factor out  (2 sin x - 1)  from both terms.

(2 sin x - 1)(3 sin x - cos x)  =  0

hectictar  Jun 27, 2017

### 5 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details