Respuesta :
Using a trigonometric identity, it is found that the sine of the angle is given as follows:
[tex]\sin{\theta} = -\frac{4}{5}[/tex].
Which trigonometric identity relates the sine and the cosine of an angle?
Considering an angle [tex]\theta[/tex], the identity is given as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
In this problem, the cosine is given as follows:
[tex]\cos{\theta} = \frac{3}{5}[/tex]
Hence the sine is found as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
[tex]\sin^2{\theta} + \left(\frac{3}{5}\right)^2{\theta} = 1[/tex]
[tex]\sin^2{\theta} + \frac{9}{25} = 1[/tex]
[tex]\sin^2{\theta} = \frac{16}{25}[/tex]
[tex]\sin{\theta} = \pm \sqrt{\frac{16}{25}}[/tex]
In quadrant IV, the sine is negative, hence:
[tex]\sin{\theta} = -\frac{4}{5}[/tex].
More can be learned about trigonometric identities at https://brainly.com/question/7331447
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