Posted by **Matthew** on Tuesday, December 4, 2012 at 4:46pm.

Write the following trigonometric expression as an algebraic expression in x free of trigonometric or inverse trigonometric functions

sin(cos^-1 x) -1≤x≤1

- TRIGONOMETRY -
**Steve**, Tuesday, December 4, 2012 at 4:58pm
draw a triangle with adjacent/hypotenuse = x/1

the other leg is √(1-x^2)

so, sin(arccos(x)) = √(1-x^2)

or, if θ = arccos(x), then we have the ubiquitous identity

sin^2θ + cos^2θ = 1

but cosθ = x, so

sin^2θ + x^2 = 1

sin^2θ = 1-x^2

sinθ = √(1-x^2)

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