What is the value of arcsin(tan(-pi/4)) ?

The value of arcsin(tan(-pi/4)) is -pi/2

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arcsin(tan(-pi/4))

arcsin (tan (- \frac{π}{4}))

- \frac{π}{2}

Solution steps

arcsin (tan (- \frac{π}{4}))

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{π}{4}) = - tan (\frac{π}{4})

= arcsin (- tan (\frac{π}{4}))

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- tan (\frac{π}{4})) = - arcsin (tan (\frac{π}{4}))

= - arcsin (tan (\frac{π}{4}))

Rewrite using trig identities:

arcsin (tan (\frac{π}{4})) = \frac{π}{2}

= - \frac{π}{2}

arcsin (\frac{- 2}{3})

2 cos^{2} (\frac{7 π}{12}) - 1

arctan (\frac{1}{1.5})

sin^{2} (30 0^{\circ})

arctan (\frac{- 4}{- 2})

What is the value of arcsin(tan(-pi/4)) ?
The value of arcsin(tan(-pi/4)) is -pi/2