Question

Let cos A =
`1/√(10)` with A in QI and find sin(2A)

Answer 1

hope this pic helps. enjoy

Answer 2

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Answer:

sin(2A) = 0.6

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):

`sin((A))=\sqrt{1-(1)/((√(10))^2)}=\sqrt{(9)/(10)}=(3)/(√(10))\\\\sin((2A))=2sin((A))cos((A))=2\cdot(3)/(√(10))\cdot(1)/(√(10))\\\\\boxed{sin((2A))=(6)/(10)=0.6}`

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Alternate solution

Your calculator can also find this for you:

sin(2A) = sin(2·arccos(1/√10)) = 0.6