Solve 2 sin x - 1=0 for 0 < or equal to x< 2 pi.?

Answer 1

2 sin x-1=0
2 sin x=1
sin x=.5
x=π/6, 5π/6

Answer 2

2sin(x) - 1 = 0

Your first step is to isolate sin(x). This is accomplished by first bringing the -1 to the right hand side

2sin(x) = 1

And then dividing both sides by 2

sin(x) = 1/2

Now at this point, here is where you ask yourself. On that unit circle graph you were asked to memorize, where is sine equal to 1/2? The answer to this question are two points? pi/6 and 5pi/6

Therefore

x = pi/6, 5pi/6

Answer 3

that's extremely undemanding in case you remember and attempt to coach your trigonometric regulations tan x = sinx/cosx precise? basically anticipate that (pi + x) = is an perspective image like theta Then, rewrite the equation from discovered ideas as: (sin(pi+x)/cos(pi+x)) + 2sin(pi+x) = 0 make the expression above into one fraction with a topic-unfastened denominator. you're able to have: (sin(pi+x) + 2sin(pi+x)Cos(pi+x))/cos(pi + x) you're able to desire to remind your self, however, this is not needed for this reason that cos(pi + x) interior the denominator might desire to not equivalent to 0; or you're able to finally end up with an blunders. With being reported, in undemanding terms concentration and resolve the numerator via factoring out sin(pi + x). sin(pi+x)(a million + 2cos(pi + x)) = 0 sin(pi + x) = 0 pi + x = 0, pi, 2pi x = -pi, 0, pi ______________________________________... a million + 2cos(pi + x) = 0 cos(pi + x) = -a million/2 arccos(-a million/2) in accordance to the 30-60-ninety triangle is 60 or pi/3 and cosx is barely detrimental interior the II and III quadrants the place 60 will become a hundred and twenty and 240 or 2pi/3 and 4pi/3 respectively. pi + x = 2pi/3, 4pi/3 x = (2pi/3 - pi), (4pi/3 - pi) x = -pi/s, pi/3 reject the detrimental because of shrink above and choose pi/3. the place is cosx helpful different than for I quadrants? definite, interior the fourth quadrants the place the attitude is 3 hundred or 5pi/3. So the respond is two). i wish this helps.

Answer 4

2sin(x) = 1

sin(x) = 1/2

x = arcsin(1/2) = pi/6 or 5(pi/6)