What is the value of arcsin(cos((7pi)/4)) ?

The value of arcsin(cos((7pi)/4)) is pi/4

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arcsin(cos((7pi)/4))

arcsin (cos (\frac{7 π}{4}))

\frac{π}{4}

Decimal Notation

45

Solution steps

arcsin (cos (\frac{7 π}{4}))

Rewrite using trig identities:

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

cos (\frac{7 π}{4})

sin (\frac{π}{2} - x) = cos (x)

= sin (\frac{π}{2} - \frac{7 π}{4})

= sin (- \frac{5 π}{4})

= arcsin (sin (- \frac{5 π}{4}))

Use the inverse trig property:

\frac{π}{4}

arcsin (sin (- \frac{5 π}{4}))

For

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

Rewrite using trig identities:

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

sin (- \frac{5 π}{4})

sin (x) = sin (π - (x))

= sin (\frac{5 π}{4} - π)

= sin (\frac{π}{4})

= arcsin (sin (\frac{π}{4}))

- \frac{π}{2} \leq \frac{π}{4} \leq \frac{π}{2}

= \frac{π}{4}

= \frac{π}{4}

cos (3 5^{\circ}) sin (5 5^{\circ}) + sin (3 5^{\circ}) cos (5 5^{\circ})

sin (2) (\frac{3}{5})

sin^{2} (\frac{1}{2} arccos (\frac{4}{5}))

arcsin (\frac{37}{64})

- 3 cos (\frac{π}{4})

What is the value of arcsin(cos((7pi)/4)) ?
The value of arcsin(cos((7pi)/4)) is pi/4