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}

Decimal Notation

135

Solution steps

arccos (sin (arctan (- 1)))

Rewrite using trig identities:

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

Use the following identity:

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

= \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}

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

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \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