Sin theta /x = cos theta /y then sin theta - cos theta=?

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Answer 1 · 2018-04-19T17:27:04

If # frac{ \sin theta }{x} = frac{ cos theta]{ y} # then # \sin theta - cos theta = \pm frac {x - y}{sqrt{x^2+y^2}} #

# frac{ \sin theta }{x} = frac{ cos theta]{ y} #

# frac{ \sin theta}{\cos theta } = frac{x}{y} #

# \tan \theta = x/y #

That's like a right triangle with opposite #x# and adjacent #y# so

#cos theta = frac{\pm y}{sqrt{x^2 + y^2} #

# sin theta = \tan \theta \cos theta #

# \sin theta - cos theta#

# = tan theta \cos theta - cos theta #

# = \cos theta ( \tan theta - 1) #

# = frac{\pm y}{sqrt{x^2 + y^2}} (x/y -1) #

# \sin theta - cos theta = \pm frac {x - y}{sqrt{x^2+y^2}} #