1 Answer

Olllejik · Answer 1 · 2020-07-10T08:05:17+0000

Answer:

Option B
(24)/(25)

Explanation:

we know that

$sin(2\theta) = 2 sin(\theta) cos(\theta)$

In this problem we have

$cos(\theta)=(4)/(5)$

Find the value of
$sin(\theta)$

Remember that

$sin^(2) (\theta)+cos^(2) (\theta)=1$

substitute the value

$sin^(2) (\theta)+((4)/(5))^(2)=1$

$sin^(2) (\theta)=1-(16)/(25)$

$sin^(2) (\theta)=(9)/(25)$

$sin(\theta)=(3)/(5)$

Find the value of
$sin(2\theta)$

$sin(2\theta) = 2 ((3)/(5))((4)/(5))$

$sin(2\theta) = (24)/(25)$

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