Answer:
[tex]\cos\theta=-\dfrac{4}{5}[/tex]
Step-by-step explanation:
Given sine ratio:
[tex]\sin \theta=-\dfrac{3}{5}, \quad \pi \leq \theta \leq \dfrac{3\pi}{2}[/tex]
To find cos(θ), we can use the Pythagorean identity, sin²θ + cos²θ = 1.
Substitute the given value of sin(θ) into the identity and solve for cos(θ):
[tex]\left(-\dfrac{3}{5}\right)^2+\cos^2\theta=1\\\\\\\\\dfrac{9}{25}+\cos^2\theta=1\\\\\\\\\cos^2\theta=1-\dfrac{9}{25}\\\\\\\\\cos^2\theta=\dfrac{16}{25}\\\\\\\\\cos\theta=\pm\sqrt{\dfrac{16}{25}}\\\\\\\\\cos\theta=\pm\dfrac{4}{5}[/tex]
Angle θ is in the third quadrant. Since the cosine of an angle is negative in the third quadrant, we take the negative square root. Therefore:
[tex]\Large\boxed{\boxed{\cos\theta=-\dfrac{4}{5}}}[/tex]
