Question

What is the value of Arc cosine (negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction)?

Answer 1

The value of arccos(-√3/2) is 5π/6.

In the given question,

We have to find the value of $arccos(-\frac{\sqrt{3}}{2})$.

The given term is $arccos(-\frac{\sqrt{3}}{2})$.

We using the quadrant rule.

The value is in negative so we check in which quadrant the value of cos negative.

As we now that in second quadrant only the value of sine and cosine is positive and all value are negative.

The second quadrant of 180 degree or we can also write 180 degree as π.

From the trigonometry table we know that at 30 degree or (π/6) the value of cos is √3/2.

So the value of cos at which -√3/2 is

-√3/2 = cos(π - π/6)

-√3/2 = cos(π×6/6 - π/6)

-√3/2 = cos(6π/6 - π/6)

-√3/2 = cos{(6π- π)/6}

-√3/2 = cos 5π/6

So we can write it as

arccos(-√3/2)=arccos(cos 5π/6)

Since there is a arccos and cos both so only left 5π/6.

arccos(-√3/2)=5π/6

Hence, the value of arccos(-√3/2) is 5π/6.

To learn more about trigonometry quadrant  link is here

brainly.com/question/7196312

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