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)

## Answer this Question

## Related Questions

- tRiG/ AlGeBrA - 1) Use double-angle identities to write the following expression...
- trig - 1) Use double-angle identities to write the following expression, using ...
- precal - use a right triangle to write the expression as an algebraic expression...
- Pre-Calc - I am really struggling with how to do these problems, I posted them a...
- Pre-Calc - 1) Use an Addition or Subtraction Formula to write the expression as ...
- Math(Correction) - Use the given function values and trigonometric identities (...
- Math(Correction) - Use the given function values and trigonometric identities (...
- Math - Use the given function values and trigonometric identities (including ...
- Trigonometry - Write the trigonometric expression as an algebraic expression. 1...
- Pre Calclulus - Write the trigonometric expression as an algebraic expression. ...

More Related Questions