What is the value of arcsin(cos(pi/9)) ?

The value of arcsin(cos(pi/9)) is (7pi)/(18)

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arcsin(cos(pi/9))

arcsin (cos (\frac{π}{9}))

\frac{7 π}{18}

Decimal Notation

70

Solution steps

arcsin (cos (\frac{π}{9}))

Rewrite using trig identities:

cos (\frac{π}{9}) = sin (\frac{7 π}{18})

cos (\frac{π}{9})

sin (\frac{π}{2} - x) = cos (x)

= sin (\frac{π}{2} - \frac{π}{9})

= sin (\frac{7 π}{18})

= arcsin (sin (\frac{7 π}{18}))

Use the inverse trig property:

\frac{7 π}{18}

arcsin (sin (\frac{7 π}{18}))

For

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

- \frac{π}{2} \leq \frac{7 π}{18} \leq \frac{π}{2}

= \frac{7 π}{18}

= \frac{7 π}{18}

2 sec^{2} (\frac{π}{4})

csc (- 22 5^{\circ})

arccos (0.707)

cos (\frac{2 π}{6})

2 sin (7 5^{\circ}) cos (7 5^{\circ})

What is the value of arcsin(cos(pi/9)) ?
The value of arcsin(cos(pi/9)) is (7pi)/(18)