How do you evaluate $arcsin (sin 3)$ $arcsin(sin3)$ ?

Question

How do you evaluate $arcsin (sin 3)$ $arcsin(sin3)$ ?

1 Answer

Impact of this question

14489 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-21T08:25:13

$arcsin (sin (3)) = π - 3$ $arcsin(sin(3))=pi-3$

Explanation:

Note that $arcsin$ $arcsin$ maps $[- 1, 1]$ $[-1,1]$ to $[- \frac{π}{2}, \frac{π}{2}]$ $[-pi/2,pi/2]$ .

We need to find an angle $x \in [- \frac{π}{2}, \frac{π}{2}]$ $x in [-pi/2,pi/2]$ where $sin (x) = sin (3)$ $sin(x)=sin(3)$ .

Since $sin (x)$ $sin(x)$ is symmetric about $x = \frac{π}{2}$ $x=pi/2$ we have $sin (3) = sin (π - 3)$ $sin(3)=sin(pi-3)$ . $π - 3$ $pi-3$ is in $[- \frac{π}{2}, \frac{π}{2}]$ $[-pi/2,pi/2]$ , therefore we have:

$arcsin (sin (3)) = π - 3$ $arcsin(sin(3))=pi-3$

Science

Math

Humanities

... and beyond

How do you evaluate $arcsin (sin 3)$ $arcsin(sin3)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you evaluate arcsin(sin3)arcsin(sin3)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you evaluate $arcsin (sin 3)$ $arcsin(sin3)$ ?