What is the value of arcsin(sin(-(8pi)/5)) ?

The value of arcsin(sin(-(8pi)/5)) is (2pi)/5

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arcsin(sin(-(8pi)/5))

arcsin (sin (- \frac{8 π}{5}))

\frac{2 π}{5}

Decimal Notation

72

Solution steps

arcsin (sin (- \frac{8 π}{5}))

Use the inverse trig property:

\frac{2 π}{5}

arcsin (sin (- \frac{8 π}{5}))

For

- \frac{π}{2} \leq x \leq \frac{π}{2}, a rcs in (s in (x)) = x

Rewrite using trig identities:

sin (- \frac{8 π}{5}) = sin (\frac{2 π}{5})

sin (- \frac{8 π}{5})

sin (x + 2 π \cdot k) = sin (x)

= sin (- \frac{8 π}{5} + 1 \cdot 2 π)

= sin (\frac{2 π}{5})

= arcsin (sin (\frac{2 π}{5}))

- \frac{π}{2} \leq \frac{2 π}{5} \leq \frac{π}{2}

= \frac{2 π}{5}

= \frac{2 π}{5}

sec (arctan (- 4))

\frac{cos ( 3 0 ^{\circ} ) + tan ( 6 0 ^{\circ} )}{2 - cos ^{2} ( 4 5 ^{\circ} )}

sin (\frac{arctan ( \frac{4}{3} )}{2})

cos (30 5^{\circ})

2 cos^{2} (0.19) - 1

What is the value of arcsin(sin(-(8pi)/5)) ?
The value of arcsin(sin(-(8pi)/5)) is (2pi)/5