How do you calculate #sin ( sin^ -1 ( 3/8))#?

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Answer 1 · 2018-05-20T08:11:54

#color(purple)(=> 0.375529^c# or #color(brown)(21.5^@#

#sin (sin ^-1 (3/8)#

#sin^-1 (3/8) = 0.384397#

#=> sin (0.384397)#

#color(purple)(=> 0.375529^c# or #color(brown)(21.5^@#

Answer 2 · 2018-05-24T17:20:16

#sin arcsin(3/8) = 3/8#

I never use the #-1# power notation for the inverse trig functions -- it's awful.

I treat #arcsin(x) # as a multivalued expression, all the angles whose sine is #x.#

Even though #arcsin(x)# is multivalued, there's only one value for it's sine,

#sin arcsin x = x#

Here

#sin arcsin(3/8) = 3/8#