Respuesta :

LammettHash
[tex]\sin240^\circ=\sin(180-240)^\circ=\sin(-60^\circ)=-\sin60^\circ=-\dfrac{\sqrt3}2[/tex]

using the fact that (1) [tex]\sin x=\sin(\pi -x)[/tex] (where [tex]x[/tex] is in radians; replace with [tex]180^\circ[/tex] to convert to degrees) and (2) [tex]\sin(-x)=-\sin x[/tex] for all [tex]x[/tex]. Then [tex]\sin\dfrac\pi3=\sin60^\circ[/tex] is a known value.
aachen

Answer:

[tex]-\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

We need to find the value of 240°

To find the value, first we need to understand in which quadrant 240° lies.

We know that there are four quadrants.

First quadrant lies from [tex](0,\:\frac{\pi }{2})[/tex] in radians or 0 to 90° in degrees.

Second quadrant lies from [tex](\frac{\pi }{2},\:\pi)[/tex] in radians or 90° to 180° in degrees.

Third quadrant lies from [tex](\pi,\:\frac{3\pi }{2})[/tex] in radians or  180° to 270° in degrees.

Fourth quadrant lies from [tex](\frac{3\pi }{2},\:}2\pi )[/tex] in radians or  270° to 360° in degrees.

Clearly we can see that 240° lies in the third quadrant, and in the third quadrant sin theta is negative.

Now, [tex]\text{sin\:240}^{\circ}=\text{sin\:(180+60)}^{\circ}[/tex]

We know that [tex]\text{sin}(\pi +x)=-\text{sin}x[/tex]

So,  [tex]\text{sin\:240}^{\circ}=-\text{sin\:60}^{\circ}[/tex]

Hence, [tex]\text{sin\:240}^{\circ}=-\frac{\sqrt{3}}{2}[/tex]