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

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

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arccos(sin((3pi)/4))

arccos (sin (\frac{3 π}{4}))

\frac{π}{4}

Decimal Notation

45

Solution steps

arccos (sin (\frac{3 π}{4}))

Rewrite using trig identities:

sin (\frac{3 π}{4}) = sin (\frac{π}{4})

sin (\frac{3 π}{4})

Use the basic trigonometric identity:

sin (x) = sin (π - x)

= sin (π - \frac{3 π}{4})

Simplify:

π - \frac{3 π}{4} = \frac{π}{4}

π - \frac{3 π}{4}

Convert element to fraction:

π = \frac{π 4}{4}

= \frac{π 4}{4} - \frac{3 π}{4}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π 4 - 3 π}{4}

Add similar elements:

4 π - 3 π = π

= \frac{π}{4}

= sin (\frac{π}{4})

= arccos (sin (\frac{π}{4}))

Rewrite using trig identities:

sin (\frac{π}{4}) = cos (\frac{π}{4})

sin (\frac{π}{4})

cos (\frac{π}{2} - x) = sin (x)

= cos (\frac{π}{2} - \frac{π}{4})

= cos (\frac{π}{4})

= arccos (cos (\frac{π}{4}))

Use the inverse trig property:

\frac{π}{4}

arccos (cos (\frac{π}{4}))

For

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

0 \leq \frac{π}{4} \leq π

= \frac{π}{4}

= \frac{π}{4}

cos (\frac{π}{9}) cos (\frac{2 π}{9}) - sin (\frac{π}{9}) sin (\frac{2 π}{9})

csc (3 9^{\circ})

24 tan (7 0^{\circ})

arctan (\frac{60}{40})

sin (\frac{5 π}{5})

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