What is the value of arccos(sin((7pi)/4)) ?

The value of arccos(sin((7pi)/4)) is (3pi)/4

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arccos(sin((7pi)/4))

arccos (sin (\frac{7 π}{4}))

\frac{3 π}{4}

Decimal Notation

135

Solution steps

arccos (sin (\frac{7 π}{4}))

Rewrite using trig identities:

sin (\frac{7 π}{4}) = cos (- \frac{5 π}{4})

sin (\frac{7 π}{4})

cos (\frac{π}{2} - x) = sin (x)

= cos (\frac{π}{2} - \frac{7 π}{4})

= cos (- \frac{5 π}{4})

= 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 + 2 π \cdot k) = cos (x)

= cos (- \frac{5 π}{4} + 1 \cdot 2 π)

= 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}

cos (arccos (π))

arctan (tan (\frac{7 π}{4}))

cot (- 9 0^{\circ})

tan (6 7^{\circ})

- cos (\frac{2 π}{3})

What is the value of arccos(sin((7pi)/4)) ?
The value of arccos(sin((7pi)/4)) is (3pi)/4