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}

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}

= - \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