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Refresh my memory , Inverse Trig

  • Thread starter rocomath
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Refresh my memory plz, Inverse Trig

[tex]x=\sin^{-1}\left(-\frac{\sqrt{2}}{2}\right)[/tex]

Inverse sine is defined from [tex]-\frac{\pi}{2}[/tex] to [tex]\frac{\pi}{2}[/tex] which lies in the 1st and 4th quadrant.

So [tex]x=-\frac{\pi}{4}[/tex]
 

Answers and Replies

dynamicsolo
Homework Helper
1,648
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[tex]x=\sin^{-1}\left(-\frac{\sqrt{2}}{2}\right)[/tex]

Inverse sine is defined from [tex]-\frac{\pi}{2}[/tex] to [tex]\frac{\pi}{2}[/tex] which lies in the 1st and 4th quadrant.

So [tex]x=-\frac{\pi}{4}[/tex]
Correct -- and your calculator and mine will back you up on that...
 
1,750
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Correct -- and your calculator and mine will back you up on that...
That's the thing, it gives me different answers. (in radians)

[tex]\sin^{-1}\left(-\frac{1}{\sqrt 2}\right)\approx -0.785[/tex]

[tex]\sin\left(-\frac{\pi}{4}\right)\approx -0.707[/tex]
 
458
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Those aren't different answers. -pi / 4 is -0.785 and -1/ root 2 is -0.707.

The inverse sin of the ratio will give you the angle, the sin of the angle will give you the ratio.
 
dynamicsolo
Homework Helper
1,648
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That's the thing, it gives me different answers. (in radians)

[tex]\sin^{-1}\left(-\frac{1}{\sqrt 2}\right)\approx -0.785[/tex]

[tex]\sin\left(-\frac{\pi}{4}\right)\approx -0.707[/tex]
And -45º converted to radians is? (In other words, what's [tex]\frac{-\pi}{4}[/tex]?)

[I expect we're going to hear a "D'oh!" in 3, 2, 1, ...]
 
Last edited:
1,750
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And -45º converted to radians is? (In other words, what's [tex]\frac{-\pi}{4}[/tex]?)

[I expect we're going to hear a "D'oh!" in 3, 2, 1, ...]
LOL, I know that ... but what's with the calculator? Am I putting it in right?
 
dynamicsolo
Homework Helper
1,648
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LOL, I know that ... but what's with the calculator? Am I putting it in right?
Of course you are! The sine of -45º or -pi/4 radians (which is approximately -0.785398... radians) gives you -1/sqrt(2) =
-[sqrt(2)]/2 = -0.70710678... ,
so taking the arcsine of (-0.70710678...) should give you
-0.785398....

I guess we're puzzled why you're puzzled. There's no reason you should get the same number in both directions. The magnitude of arcsin(x) doesn't match the magnitude of sin(x) at x = (pi)/4 ...
 
1,750
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LMAO ... omg, I crack myself up :)
 

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