Find $arcsin (- \frac{\sqrt{3}}{2})$ $arcsin(-sqrt3/2)$ ?

Question

Find $arcsin (- \frac{\sqrt{3}}{2})$ $arcsin(-sqrt3/2)$ ?

3 Answers

Impact of this question

28616 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-12T06:52:51

$arcsin (- \frac{\sqrt{3}}{2})$ $arcsin(-sqrt3/2)$ is equal to $(2 n + 1) π \pm \frac{π}{3}$ $(2n+1)pi+-pi/3$ , where $n$ $n$ is an integer

Explanation:

$arcsin (- \frac{\sqrt{3}}{2})$ $arcsin(-sqrt3/2)$ is the angle whose sine is $- \frac{\sqrt{3}}{2}$ $-sqrt3/2$ .

As sine is negative in second and third quadrant and $sin (\frac{π}{3}) = \frac{\sqrt{3}}{2}$ $sin(pi/3)=sqrt3/2$ ,

we have $sin (π - \frac{π}{3}) = - \frac{\sqrt{3}}{2}$ $sin(pi-pi/3)=-sqrt3/2$ and

$sin (p + \frac{π}{3}) = - \frac{\sqrt{3}}{2}$ $sin(p+pi/3)=-sqrt3/2$

Hence $arcsin (- \frac{\sqrt{3}}{2})$ $arcsin(-sqrt3/2)$ is equal to $\frac{2 π}{3}$ $(2pi)/3$ or $\frac{4 π}{3}$ $(4pi)/3$ .

As adding or subtracting $2 π$ $2pi$ does not affect trigonometric ratios of angles, we can have infinite solutions given by

$(2 n + 1) π \pm \frac{π}{3}$ $(2n+1)pi+-pi/3$ , where $n$ $n$ is an integer.

Answer 2 · 2016-04-12T07:26:37

$n π + {(- 1)}^{n} (- \frac{π}{3})$ $npi+(-1)^n(-pi/3)$ , n = 0, 1, 2, 3,...

Explanation:

If sin x = a and $α$ $alpha$ is the principal value of $x \in [- \frac{π}{2}, \frac{π}{2}]$ $x in [-pi/2, pi/2]$ , then the general value of x = $n π + {(- 1)}^{n} α$ $npi+(-1)^nalpha$ , n = 0, 1, 2, 3,...

Here $x = a r c sin (- \frac{\sqrt{3}}{2})$ $x = arc sin (-sqrt3/2)$
$sin x = - \frac{\sqrt{3}}{2}$ $sin x = -sqrt3/2$ .
So, $α = - \frac{π}{3}$ $alpha = -pi/3$ ..

The answer is as stated.

Answer 3 · 2018-05-20T05:42:46

$x = \frac{4 π}{3} + 2 k π$ $x = (4pi)/3 + 2kpi$
$x = \frac{5 π}{3} + 2 k π$ $x = (5pi)/3 + 2kpi$

Explanation:

$sin x = (- \frac{\sqrt{3}}{2})$ $sin x = (-sqrt3/2)$ . Find arc x (or angle x)
Unit circle gives 2 solutions for arc x (or angle x) -->
$x = - \frac{π}{3} + 2 k π$ $x = - pi/3 + 2kpi$ , and
$x = π - (- \frac{π}{3}) = π + \frac{π}{3} = \frac{4 π}{3} + 2 k π$ $x = pi - (-pi/3) = pi + pi/3 = (4pi)/3 + 2kpi$
Note that $x = - \frac{π}{3}$ $x = -pi/3$ is co-terminal to $x = \frac{5 π}{3} .$ $x = (5pi)/3.$
Answers:
$x = \frac{4 π}{3} + 2 k π$ $x = (4pi)/3 + 2kpi$
$x = \frac{5 π}{3} + 2 k π$ $x = (5pi)/3 + 2kpi$

Science

Math

Humanities

... and beyond

Find $arcsin (- \frac{\sqrt{3}}{2})$ $arcsin(-sqrt3/2)$ ?

3 Answers

Explanation:

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Find arcsin(−√32)arcsin(-sqrt3/2)?

3 Answers

Explanation:

Explanation:

Explanation:

Related questions

Impact of this question

Find $arcsin (- \frac{\sqrt{3}}{2})$ $arcsin(-sqrt3/2)$ ?