SOLUTION: please help me solve these questions: Find an algebraic expression for the given f functions of x. (a) Y = cos (sin-1 x) (b) Y = sin (2 sin-1 x)

Question 521638: please help me solve these questions: Find an algebraic expression for the given f
functions of x. (a) Y = cos (sin-1 x)
(b) Y = sin (2 sin-1 x)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
please help me solve these questions: Find an algebraic expression for the given f
functions of x. (a) Y = cos (sin-1 x)
(b) Y = sin (2 sin-1 x)
**
(a) y=cos (sin-1 x)
(sin-1 x) is an angle whose sin=x/1=opposite side/hypotenuse
The adjacent side,by Pythagorean Theorem, therefore, is √(1-x^2)
cos of the angle, then=adjacent side/hypotenuse=√(1-x^2)/1=√(1-x^2)
y = cos (sin-1 x)=√(1-x^2)
..
(b) Y = sin (2 sin-1 x)
2 sin-1 x is twice an angle whose sin=x and cosx=√(1-x^2)
Identity: sin 2x=2 sinxcosx
y = sin (2 sin-1 x)=sin2x=2sinxcosx=2x√(1-x^2)
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