4 sin2x= - 3sinx?

Question

also:
8cotx=-10
how do i do this?
ive been trying for 20 minutes and nothings working!
thanksss

for the first one, can you add 3sinx to both sides or is that brekaing some rule since theyre not technically liek terms since the other one is 2x not x.

Answer 1

Question 1
8 sin x cos x + 3sin x = 0
(sin x) (8 cos x + 3) = 0
sin x = 0 , cos x = - 3 / 8
x = 0° , 180° , 360° , 112° , 292°

Question 2
cot x = - 10 / 8
1 / tan x = - 10 / 8
tan x = - 4 / 5
x = 141.3° , 321.3°

Answer 2

hello!
what you mentioned in the additional details is correct. you cannot combine both terms (2x) and (x). express sin 2x as 2 sinx cosx, so you get:
4(2sinxcosx)=-3sinx now divide both sides by -3 sinx;
-8/3 cos x = 1; and thus cosx= -3/8. using your scientific calculator, use the inverse cosine (arccos) function, and thus the angle with a cosine value of -3/8 is around 112.02 degrees, for the values of x between 0 and 180 degrees.
i hope this helps.
as for the second equation, simply divide both sides by 8, and you get cotx = -10/8. get the reciprocal of cot x, and you tanx = -8/10 or -4/5. using your scientific calculator again, or a table of trig values, x will be approximately equal to -38.66 degrees.

Answer 3

use the double angle formula sin2x = 2sinxcosx

4sin2x + 3sinx = 0
8sinxcosx + 3sinx = 0
sinx (8cosx + 3) = 0
sinx = 0, x = 0 or pi

cosx = 3/8, x = 68 deg
cosx = -3/8 x = 112 or 248 deg


cotx = -10/8
tan x = -8/10 x = arctan -0.8 = -38.6 deg

Answer 4

Easiest way to obtain a numerical answer is to plot both graphs on the graphics calculator and find the point of intersection.

However, for a full solution use the double angle formula:
sin(2x) = 2sin(x)cos(x)

Therefore:
4sin(2x) = -3sin(x)
8sin(x)cos(x) = -3sin(x)
8cos(x) = -3 except where sin(x)=0
x = arccos(-3/8) or x = arcsin(0)

Within the domain [0,2Pi]:
x = {0, 1.955, Pi, 4.328, 2Pi}