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if sin theta = 4/9, then what is the value of sin (π- theta)?

Sagot :

To answer this question, we need to use the inverse function of sin, that is, arcsin or sin^-1 to find the value of the angle for which sin(theta) = 4/9. Then, we have:

[tex]\sin (\theta)=\frac{4}{9}\Rightarrow\arcsin (\sin (\theta))=\arcsin (\frac{4}{9})[/tex]

Then, we have:

[tex]\theta=\arcsin (\frac{4}{9})\Rightarrow\theta=0.460553991681[/tex]

This angle is in radians. Now, we need to find the value for sin (pi - theta) as follows:

[tex]\sin (\pi-0.460553991681)=0.44444444444\ldots[/tex]

Now, we know this periodical decimal expression is equal to:

[tex]undefined[/tex]

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