9514 1404 393
Answer:
sin(2A) = 0.6
Step-by-step explanation:
A couple of trig identities are involved:
sin(α) = √(1 -cos(α)²)
sin(2α) = 2sin(α)cos(α)
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First, we need to find sin(A):
[tex]\sin{(A)}=\sqrt{1-\dfrac{1}{(\sqrt{10})^2}}=\sqrt{\dfrac{9}{10}}=\dfrac{3}{\sqrt{10}}\\\\\sin{(2A)}=2\sin{(A)}\cos{(A)}=2\cdot\dfrac{3}{\sqrt{10}}\cdot\dfrac{1}{\sqrt{10}}\\\\\boxed{\sin{(2A)}=\dfrac{6}{10}=0.6}[/tex]
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Alternate solution
Your calculator can also find this for you:
sin(2A) = sin(2·arccos(1/√10)) = 0.6
