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Doss [256]
3 years ago
12

If cos(θ)=2853 with θin Q IV, what is sin(θ)?

Mathematics
1 answer:
marysya [2.9K]3 years ago
7 0

Answer: \sin \theta=\frac{-45}{53}

Step-by-step explanation:

Since we have given that

\cos\theta=\frac{28}{53}

And we know that θ is in the Fourth Quadrant.

So, Except cosθ and sec θ, all trigonometric ratios will be negative.

As we know the "Trigonometric Identity":

\cos^2\theta+\sin^2\theta=1\\\\\sin \theta=\sqrt{1-\cos^2\theta}\\\\\sin \theta=\sqrt{1-(\frac{28}{53})^2}=\sqrt{\frac{53^2-28^2}{53^2}}\\\\\sin \theta=\sqrt{\frac{2025}{53^2}}\\\\\sin \theta=\frac{45}{53}

It must be negative due to its presence in Fourth quadrant.

Hence, \sin \theta=\frac{-45}{53}

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