The required value of [tex]sin\theta = -\frac{56}{33}[/tex].
Let , [tex]x = \frac{33}{65}[/tex] be the x-coordinate of the point P(x, y).
The p is in 4th quadrant.
According to the question.
Terminal Point on the Unit Circle states that the terminal point on the unit circle, start at (1,0), measure the angle in degree or radian on the circle (move counter clockwise if the angle is positive and clockwise if the angle is negative.)
The coordinate of the endpoint is called the terminal point.
General equation of unit circle is,
[tex]x^{2} + y^{2} = 1[/tex]
[tex]y^{2} = 1 - x^{2} \\\\y = \pm \sqrt{1-x^{2} }[/tex]
Substitute [tex]x = \frac{33}{65}[/tex] in the equation,
[tex]y = \sqrt{1-(\frac{33}{65} )^{2} }[/tex]
[tex]y = \sqrt{1-\frac{1089}{4225} } \\\\y = \sqrt{\frac{4225 - 1089}{4225} } \\\\y = \sqrt{\frac{3136}{4225} } \\\\y = \frac{56}{65}[/tex]
Now ,
[tex]sin\theta = \frac{y}{x} \\\\sin\theta = \frac{\frac{56}{65} }{\frac{33}{65} } \\\\sin\theta = \frac{56}{33}[/tex]
P lies in the fourth quadrant, you know the sine is negative.
[tex]sin\theta = -\frac{56}{33}[/tex]
Hence, The required value of [tex]sin\theta = -\frac{56}{33}[/tex].
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https://brainly.com/question/11833983
