What is the value of arccos(cos(-(19pi)/(10))) ?

The value of arccos(cos(-(19pi)/(10))) is pi/(10)

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arccos(cos(-(19pi)/(10)))

arccos (cos (- \frac{19 π}{10}))

\frac{π}{10}

Decimal Notation

18

Solution steps

arccos (cos (- \frac{19 π}{10}))

Use the inverse trig property:

\frac{π}{10}

arccos (cos (- \frac{19 π}{10}))

For

0 \leq x \leq π, a rccos (cos (x)) = x

Rewrite using trig identities:

cos (- \frac{19 π}{10}) = cos (\frac{π}{10})

cos (- \frac{19 π}{10})

cos (x + 2 π \cdot k) = cos (x)

= cos (- \frac{19 π}{10} + 1 \cdot 2 π)

= cos (\frac{π}{10})

= arccos (cos (\frac{π}{10}))

0 \leq \frac{π}{10} \leq π

= \frac{π}{10}

= \frac{π}{10}

sin (\frac{- 19 π}{6})

sin (6 0^{\circ}) + sin (4 5^{\circ})

sin (\frac{π}{4}) + 2

\frac{15}{tan ( 5 0 ^{\circ} )}

\frac{1 + cot ^{2} ( 3 0 ^{\circ} )}{1 + tan ^{2} ( 3 0 ^{\circ} )}

What is the value of arccos(cos(-(19pi)/(10))) ?
The value of arccos(cos(-(19pi)/(10))) is pi/(10)