The value of sin theta is negative root 2 divided by 2 and tan theta is -1 in the (3pi)/2 < theta < 2pi.
We know that the
[tex]cos\theta=\frac{adjacent side}{hypotenuse}[/tex]
We have
[tex]cos\theta=\frac{\sqrt{2} }{2}[/tex]
Therefore aducent side=root 3 and hypotenous=2
By usingthe pythagorus theorem
We have
[tex]adjacent \ side ^2+opposite \ side ^2=hypotenuse ^2[/tex]
[tex]\sqrt{2}^2+opp.side=2^2 \\2+opp.side^2=4\\opp.side^2=2\\opp.side^2=\sqrt{2}[/tex]
What is the sin ratio?
[tex]sin \theta=\frac{opp.side}{hypotenuse}[/tex]
Therefore we get,
[tex]sin \theta=\frac{\sqrt{2} }{2}[/tex]
[tex]=-\frac{\sqrt{2} }{2}[/tex]....when (3pi)/2 < theta < 2pi
Next we have to find the tantheta
[tex]tan \theta=\frac{adjacent}{opposite}\\ =\frac{\sqrt{2} }{\sqrt{2} }\\ =1[/tex]
=-1 when (3pi)/2 < theta < 2pi
Therefore, the value of sin theta is negative root 2 divided by 2 and
tan theta is -1.
To learn more about the trigonometric ratio visit:
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