What is cos[Arcsin(-4/5)]cos[arcsin(−45)]?

1 Answer
Antoine
Jul 21, 2015

3/535

Explanation:

First consider that : epsilon=arcsin(-4/5)ε=arcsin(−45)

epsilonε simply represents an angle.

This means that we are looking for color(red)cos(epsilon)!cos(ε)!

If epsilon=arcsin(-4/5)ε=arcsin(−45) then,

=>sin(epsilon)=-4/5⇒sin(ε)=−45

To find cos(epsilon)cos(ε) We use the identity : cos^2(epsilon)=1-sin^2(epsilon)cos2(ε)=1−sin2(ε)

=>cos(epsilon)=sqrt(1-sin^2(epsilon)⇒cos(ε)=√1−sin2(ε)

=>cos(epsilon)=sqrt(1-(-4/5)^2)=sqrt((25-16)/25)=sqrt(9/25)=color(blue)(3/5)⇒cos(ε)=√1−(−45)2=√25−1625=√925=35

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