What is the value of arcsin(cos((2pi)/3)) ?

The value of arcsin(cos((2pi)/3)) is -pi/6

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arcsin(cos((2pi)/3))

arcsin (cos (\frac{2 π}{3}))

- \frac{π}{6}

Decimal Notation

- 30

Solution steps

arcsin (cos (\frac{2 π}{3}))

Rewrite using trig identities:

cos (\frac{2 π}{3}) = sin (- \frac{π}{6})

cos (\frac{2 π}{3})

sin (\frac{π}{2} - x) = cos (x)

= sin (\frac{π}{2} - \frac{2 π}{3})

= sin (- \frac{π}{6})

= arcsin (sin (- \frac{π}{6}))

Use the inverse trig property:

- \frac{π}{6}

arcsin (sin (- \frac{π}{6}))

For

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

- \frac{π}{2} \leq - \frac{π}{6} \leq \frac{π}{2}

= - \frac{π}{6}

= - \frac{π}{6}

sin (2 2^{\circ})

tan (3 1^{\circ})

sin (- 24 0^{\circ})

arctan (\frac{1}{2})

cos (arctan (2))

What is the value of arcsin(cos((2pi)/3)) ?
The value of arcsin(cos((2pi)/3)) is -pi/6