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

The value of arcsin(cos(2pi)) is pi/2

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arcsin(cos(2pi))

arcsin (cos (2 π))

\frac{π}{2}

Decimal Notation

90

Solution steps

arcsin (cos (2 π))

Rewrite using trig identities:

cos (2 π) = sin (- \frac{3 π}{2})

cos (2 π)

sin (\frac{π}{2} - x) = cos (x)

= sin (\frac{π}{2} - 2 π)

= sin (- \frac{3 π}{2})

= arcsin (sin (- \frac{3 π}{2}))

Use the inverse trig property:

\frac{π}{2}

arcsin (sin (- \frac{3 π}{2}))

For

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

Rewrite using trig identities:

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

sin (- \frac{3 π}{2})

sin (x + 2 π \cdot k) = sin (x)

= sin (- \frac{3 π}{2} + 1 \cdot 2 π)

= sin (\frac{π}{2})

= arcsin (sin (\frac{π}{2}))

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

= \frac{π}{2}

= \frac{π}{2}

arcsin (\frac{4.4}{11})

cos (\frac{\frac{2 π}{3} + 2 π}{4})

tan (arcsin (\frac{20}{29}))

cos (1 0^{\circ}) \cdot 10

csc (\frac{π}{3}) + sin (- 3 0^{\circ})