klbala2006
sin(sin^{-1} \frac{ -sqrt{3} }{ 2 }+cos^{-1} \frac{ 1 }{ 2 })
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ash2326
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@klbala2006 Do you know the range of \(\sin^{-1} x\) ?
campbell_st
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looking at it its all 4th quadrant
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klbala2006
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i need to evaluate this function .
@ash2326 no i dont
ash2326
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Do you know the range and domain of sin (x) ?
klbala2006
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@ash2326 domain of sin(x) is (R), while its range is [-1,1]
ash2326
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Good, to have the inverse of sin function, we limit it's range
domain= range of sin x= [-1, 1]
Range = \(\large [\frac{-\pi}{2}, \frac{\pi}{2}]\)
DO you get this?
klbala2006
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yes i do
ash2326
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if x is positive, then y lies in \([0, \frac {\pi}{2}]\)
if x is negative, then y lies in \([\frac{-\pi}{2}, 0)\)
Now what's \(\sin^{-1}(\frac{-\sqrt 3}{2})\) ?
klbala2006
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\[-45\]
klbala2006
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\[-\frac{ \pi }{ 4 }\] in radian
klbala2006
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@ash2326 complete please
ash2326
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Sorry, I was away. But sin (-45) is not \(\frac{-\sqrt 3}{2}\) it's, \(\frac{-1}{\sqrt 2}\).
klbala2006
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isnt it the same ?
ash2326
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What's sin 60 ?