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If cos0=3/5 and θ is in quadrant IV, sin20=?

User Pjf
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Answer:


sen(2\theta) =(24)/(25)

Explanation:

We know that
cos(\theta) =(3)/(5) and θ is in quadrant IV

To find
sin(\theta) we use the following identity


sin^2(\theta)=1-cos^2(\theta)


cos^2(\theta) =(3^2)/(5^2)


cos^2(\theta) =(9)/(25)

Then


sin^2(\theta)=1-(9)/(25)


sin^2(\theta)=(16)/(25)


sin(\theta)=\±\sqrt{(16)/(25)}

In the IV quadrant the
sin(\theta)> 0 then we take the positive solution


sin(\theta)=(4)/(5)

Finally to find
sin(2\theta) we use the following identity


sen(2\theta) = 2 sen(\theta) cos(\theta)

Finally


sen(2\theta) = 2*(4)/(5)*(3)/(5)


sen(2\theta) =(24)/(25)

User Jon Smark
by
8.8k points

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