Respuesta :

carlosego
To solve this problem you must apply the proccedure shown below:
 1. You have the following inverse trigonometric function given in the problem above:
 [tex]y=arcsin(- \sqrt{3} /2) [/tex]
 2. By definition, you have that [tex]y=arcsinx [/tex] is equivalent to [tex]siny=x [/tex] and [tex]sin(-x)=-sin(x)[/tex], therefore:
 [tex]-siny=( \sqrt{3}/2)[/tex]
 4. The value of the sine of [tex] \sqrt{3}/2[/tex] is [tex] \pi/3[/tex], therefore:
 [tex]y=- \pi/3 [/tex]
 The answer is:[tex]- \pi/3[/tex] 

Answer:

The required term is [tex]y=-\frac{\pi}{3}\pm2k\pi[/tex]

Step-by-step explanation:

Given : [tex]y=\sin^{-1}(-\frac{\sqrt3}{2} )[/tex]

To find : The general solution ?

Solution :

[tex]y=\sin^{-1}(-\frac{\sqrt3}{2})[/tex]

Can be re-written as

[tex]\sin y=-\frac{\sqrt3}{2}[/tex]

We know, [tex]\sin (\frac{\pi}{3})=\frac{\sqrt3}{2}[/tex]

[tex]\sin (y)=\sin (-\frac{\pi}{3})[/tex]

[tex]y=-\frac{\pi}{3}[/tex]

The general solution of the sine function is

[tex]y=-\frac{\pi}{3}\pm2k\pi[/tex]

Therefore, The required term is [tex]y=-\frac{\pi}{3}\pm2k\pi[/tex]      

Otras preguntas