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✯Brainly stars ✯Moderaters ✯Other best users! Q. How do you find the exact value of cos(theta) if sin(theta)= - 2/3? Explain. \sf \longrightarrow \red{ Don't \: spam}⟶Don ′ tspam Thanks! ^_^​

Answer 1

Answer:

± √5 /3

Explanation:

Given

sin θ = - 2/3

Use trignometric identity

sin² θ + cos² θ = 1

⇒ ( - 2/3 )² + cos² θ = 1

⇒ 4/9 + cos² θ = 1

⇒ cos² θ = 1 - 4/9

⇒ cos² θ = ( 9 - 4 )/9

⇒cos² θ = 5/9

Taking square root on both sides

⇒ cos θ = ± √5/ 3

Therefore the value of cos θ is ± √5 /3

Answer 2

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How do you find the exact value of cos(θ) if sin(θ)=−2/3?

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Solution

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cosθ=

3

5

or it could be cosθ=

−3

5

Explanation:

since sinθ is negative, it can be in the third or

fourth quadrant

Drawing your right-angled triangle, place your θ in

one of three corners. Your longest side will be 3 and the side opposite the θ

will be -2 . Finally, using Pythagoras theorem, your last side should be

5

Now, if your triangle was in the third quadrant, you would

have cosθ=

−3

5

since cosine is negative in the third

quadrant

But if your triangle was in the fourth quadrant, you would

have cosθ=

3

5

since cosine is positive in the fourth

quadrant