# Thread: Solving for x

1. ## Solving for x

Hey,

I can't seem to do these 3 questions on my extension 1 assignment, hopefully sOmeone here can help.

Solve for x, 0 < or = x < or = 360 give answers to nearest minute.
1. 2cos(x+10)=-1
2. 3(tanx)^2-7tanx+4=0

3. Solve sin(2x-30)=sqrt[3]/2 for -180 < or = x < or = 180

I'm abit confused, any help appreciated.

Thanks,

2. you should know that
cos x = -1/2 when x = 120

sin x = \sqrt{3}/2 when x = 60

I will solve 1.
$2 \cos (x+10) = -1 \Rightarrow \cos (x+10) = \frac{-1}{2}$

$10+x = 120 \Rightarrow x = 110$

second let tan x = y for example

$3y^2 - 7y +4 = 0$ solve for y then x will equal arctan(y)

third like the first one

3. Originally Posted by Amer
you should know that
cos x = -1/2 when x = 120

sin x = \sqrt{3}/2 when x = 60

I will solve 1.
$2 \cos (x+10) = -1 \Rightarrow \cos (x+10) = \frac{-1}{2}$

$10+x = 120 \Rightarrow x = 110$

second let tan x = y for example

$3y^2 - 7y +4 = 0$ solve for y then x will equal arctan(y)

third like the first one
I got that answer except I need all possible values of x between 0 and 360, when I try to get the numbers, things go wrong =/

4. solved all 3 problems, thanks.