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belka [17]
3 years ago
9

If cos ⁡θ=−8/17 and 180°θ < 270°, what is sin θ?

Mathematics
2 answers:
marissa [1.9K]3 years ago
8 0

Answer:

sinΘ = - \frac{15}{17}

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1

⇒ sinx = ± \sqrt{1-cos^2x}

Since 180 < Θ < 270 then sinΘ < 0

sinΘ = - \sqrt{1-(-8/17)^2}

        = - \sqrt{1-\frac{64}{289} }

        = - \sqrt{\frac{225}{289} } = - \frac{15}{17}

worty [1.4K]3 years ago
6 0
Here is your answer

[I am using ☆ instead of theta]

cos☆= -8/17

{cos}^{2}☆= {(-8/17)}^{2}= 64/289

Now,

sin☆= \sqrt{1-{cos}^{2}☆}

sin☆= \sqrt{1- (64/289)}

sin☆= \sqrt{(289-64)/289}

sin☆= \sqrt{225/289}

sin☆= 15/17

Since, 180<theta<270

so, it must lie in 3rd quadrant.

In third quadrant

sin☆ is -ve

Hence, sin☆= -15/17

HOPE IT IS USEFUL
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