Question

find the general solution of sin X=-1/2

Answer 1

sin is negative in two quadrant.third and forth.

in third quadrant sin(X)=-1/2

so sin X=sin210°

X=n210°

and forth quadrant sinX=-1/2

so sinX=sin330°

X=n330°. (where n is an integer)

Answer 2

x = nπ ± (-1)^n (7π/6)

Given

• sin X=-1/2

To find

• general solution

Solution

we are provided with a trigonometric equation and are asked to find the general solution of it that is the points at which the equation holds correct.

we know that general solution is in a form of a equation with n as a variable that varies with respect to the values in the domain.

sinx = -1/2

or, sinx = - sin30. ( in degree measure)

or, sinx = -sin(π/6) ( in radian measure)

sine function becomes negative in the third as well as 4 th quadrant therefore, we are free to choose any value of sine (quadrant) that becomes negative,

considering 3rd quadrant,

sinx = -sin(π/6)

or, sinx = sin(π+π/6)

or, sinx = sin( 7π/6)

therefore, 7π/6 is the principle solution of the given equation.

Thus, using the generally equation to find the general solution of sine function, we get,

x = nπ ± (-1)^n 7π/6