What is the value of arccos(sin(arctan(-1))) ?

The value of arccos(sin(arctan(-1))) is (3pi)/4

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arccos(sin(arctan(-1)))

arccos (sin (arctan (- 1)))

\frac{3 π}{4}

Solution steps

arccos (sin (arctan (- 1)))

Rewrite using trig identities:

sin (arctan (- 1)) = \frac{( - 1 ) 1 + ( - 1 ) ^{2}}{1 + ( - 1 ) ^{2}}

= arccos \frac{( - 1 ) 1 + ( - 1 ) ^{2}}{1 + ( - 1 ) ^{2}}

Simplify

= arccos (- \frac{2}{2})

Use the following trivial identity:

arccos (- \frac{2}{2}) = \frac{3 π}{4}

= \frac{3 π}{4}

sin (\frac{7 π}{18})

sec (3 8^{\circ})

cos (5 \cdot π)

\frac{cos ( π )}{1}

4 sin (0.25)

What is the value of arccos(sin(arctan(-1))) ?
The value of arccos(sin(arctan(-1))) is (3pi)/4