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kifflom [539]
2 years ago
14

Let cos A =

"absmiddle" class="latex-formula"> with A in QI and find sin(2A)
Mathematics
2 answers:
Orlov [11]2 years ago
7 0

Answer:

hope this pic helps. enjoy

Lyrx [107]2 years ago
5 0

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)

__

First, we need to find sin(A):

  \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}

__

<em>Alternate solution</em>

Your calculator can also find this for you:

  sin(2A) = sin(2·arccos(1/√10)) = 0.6

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