What is the value of arccos(cos((5pi)/4)) ?

The value of arccos(cos((5pi)/4)) is (3pi)/4

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arccos(cos((5pi)/4))

arccos (cos (\frac{5 π}{4}))

\frac{3 π}{4}

Decimal Notation

135

Solution steps

arccos (cos (\frac{5 π}{4}))

Use the inverse trig property:

\frac{3 π}{4}

arccos (cos (\frac{5 π}{4}))

For

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

Rewrite using trig identities:

cos (\frac{5 π}{4}) = cos (\frac{3 π}{4})

cos (\frac{5 π}{4})

cos (x) = cos (2 π - (x))

= cos (2 π - \frac{5 π}{4})

= cos (\frac{3 π}{4})

= arccos (cos (\frac{3 π}{4}))

0 \leq \frac{3 π}{4} \leq π

= \frac{3 π}{4}

= \frac{3 π}{4}

arcsin (3)

cos (0.5)

cos^{3} (π)

arccot (\frac{3}{3})

sin (34 5^{\circ})

What is the value of arccos(cos((5pi)/4)) ?
The value of arccos(cos((5pi)/4)) is (3pi)/4