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What is the exact value of sin-1(− √2/2) ? Enter your answer, in terms of π , in the box. ______radians

Sagot :

sqdancefan

Answer:

  -π/4

Step-by-step explanation:

You want the angle in radians whose sine is -(√2)/2.

Sine

You recall from memory that sin(45°) = (√2)/2, and you know the sine is negative for negative angles in the range -180° to 0°. The inverse sine function has a range of -90° to +90°, so ...

  [tex]\sin^{-1}\left(-\dfrac{\sqrt{2}}{2}\right)=-45^\circ=\boxed{-\dfrac{\pi}{4}\text{ radians}}[/tex]

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