## klbala2006 3 years ago sin(sin^{-1} \frac{ -sqrt{3} }{ 2 }+cos^{-1} \frac{ 1 }{ 2 })

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1. ash2326

@klbala2006 Do you know the range of $$\sin^{-1} x$$ ?

2. campbell_st

looking at it its all 4th quadrant |dw:1352871092096:dw|

3. klbala2006

i need to evaluate this function . @ash2326 no i dont

4. ash2326

Do you know the range and domain of sin (x) ?

5. klbala2006

@ash2326 domain of sin(x) is (R), while its range is [-1,1]

6. ash2326

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?

7. klbala2006

yes i do

8. ash2326

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 $$\sin^{-1}(\frac{-\sqrt 3}{2})$$ ?

9. klbala2006

$-45$

10. klbala2006

$-\frac{ \pi }{ 4 }$ in radian

11. klbala2006

12. ash2326

Sorry, I was away. But sin (-45) is not $$\frac{-\sqrt 3}{2}$$ it's, $$\frac{-1}{\sqrt 2}$$.

13. klbala2006

isnt it the same ?

14. ash2326

What's sin 60 ?