How do you find the exact value of $arcsin (sin (\frac{7 π}{3}))$ $arcsin(sin((7pi)/3))$ ?

Question

How do you find the exact value of $arcsin (sin (\frac{7 π}{3}))$ $arcsin(sin((7pi)/3))$ ?

1 Answer

Impact of this question

22550 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-23T12:33:01

$arcsin (sin (\frac{7 π}{3})) = \frac{π}{3}$ $arcsin(sin((7pi)/3)) = pi/3$

Explanation:

As an argument to a trigonometric function:
$XXXX$ $color(white)("XXXX")$ $\frac{7 π}{3}$ $(7pi)/3$ is equivalent to $\frac{π}{3}$ $pi/3$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ (since $\frac{7 π}{3} = 2 π + \frac{π}{3}$ $(7pi)/3 = 2pi+pi/3$ )

Provided $θ$ $theta$ is within $[0, π]$ $[0, pi]$
$XXXX$ $color(white)("XXXX")$ $arcsin (sin (θ)) = θ$ $arcsin(sin(theta)) = theta$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ (basic definition)

So
$arcsin (sin (\frac{7 π}{3}))$ $arcsin(sin((7pi)/3))$
$XXXX$ $color(white)("XXXX")$ $= arcsin (sin (\frac{π}{3}))$ $= arcsin(sin(pi/3))$
$XXXX$ $color(white)("XXXX")$ $= \frac{π}{3}$ $= pi/3$

Science

Math

Humanities

... and beyond

How do you find the exact value of $arcsin (sin (\frac{7 π}{3}))$ $arcsin(sin((7pi)/3))$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the exact value of arcsin(sin(7π3))arcsin(sin((7pi)/3))?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the exact value of $arcsin (sin (\frac{7 π}{3}))$ $arcsin(sin((7pi)/3))$ ?