What is the value of arctan(sin(-pi/2)) ?

The value of arctan(sin(-pi/2)) is -pi/4

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arctan(sin(-pi/2))

arctan (sin (- \frac{π}{2}))

- \frac{π}{4}

Decimal Notation

- 45

Solution steps

arctan (sin (- \frac{π}{2}))

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{π}{2}) = - sin (\frac{π}{2})

= arctan (- sin (\frac{π}{2}))

Use the following property:

arctan (- x) = - arctan (x)

arctan (- sin (\frac{π}{2})) = - arctan (sin (\frac{π}{2}))

= - arctan (sin (\frac{π}{2}))

Rewrite using trig identities:

arctan (sin (\frac{π}{2})) = \frac{π}{4}

arctan (sin (\frac{π}{2}))

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= arctan (1)

= arctan (1)

Use the following trivial identity:

arctan (1) = \frac{π}{4}

arctan (1)

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{4}

= \frac{π}{4}

= - \frac{π}{4}

- 3 sin (\frac{π}{6})

tan (\frac{23 π}{4})

sin^{2} (6 0^{\circ}) - cos (3 0^{\circ})

sin (arcsin (\frac{1}{6}) + arctan (- 5))

sec (arcsin (\frac{24}{25}))

What is the value of arctan(sin(-pi/2)) ?
The value of arctan(sin(-pi/2)) is -pi/4