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

The value of arccos(sin(-(5pi)/4)) is pi/4

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arccos(sin(-(5pi)/4))

arccos (sin (- \frac{5 π}{4}))

\frac{π}{4}

Decimal

45

Solution steps

arccos (sin (- \frac{5 π}{4}))

Use the following property:

sin (- x) = - sin (x)

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

= arccos (- sin (\frac{5 π}{4}))

Rewrite using trig identities:

sin (\frac{5 π}{4}) = - sin (\frac{3 π}{4})

sin (\frac{5 π}{4})

Use the following identity:

sin (x) = - sin (2 π - x)

sin (x)

Use the following property:

sin (θ) = - sin (- θ)

sin (x) = - sin (- x)

= - sin (- x)

Apply the periodicity of

sin

sin (2 π + θ) = sin (θ)

- sin (- x) = - sin (2 π - x)

= - sin (2 π - x)

= - sin (2 π - \frac{5 π}{4})

Simplify:

2 π - \frac{5 π}{4} = \frac{3 π}{4}

2 π - \frac{5 π}{4}

Convert element to fraction:

2 π = \frac{2 π 4}{4}

= \frac{2 π 4}{4} - \frac{5 π}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{2 π 4 - 5 π}{4}

2 π 4 - 5 π = 3 π

2 π 4 - 5 π

Multiply the numbers:

2 \cdot 4 = 8

= 8 π - 5 π

Add similar elements:

8 π - 5 π = 3 π

= 3 π

= \frac{3 π}{4}

= - sin (\frac{3 π}{4})

= arccos (- (- sin (\frac{3 π}{4})))

Simplify

= 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}

What is the value of arccos(sin(-(5pi)/4)) ?
The value of arccos(sin(-(5pi)/4)) is pi/4