SOLUTION: If ∠A is ACUTE and cos A = 4/5 find sin A, cos 2A, sin 2A, and tan 2A

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Question 1032481: If ∠A is ACUTE and cos A = 4/5 find sin A, cos 2A, sin 2A, and tan 2A
Answer by ikleyn(52781) About Me  (Show Source):
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If ∠A is ACUTE and cos A = 4/5 find sin A, cos 2A, sin 2A, and tan 2A
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1.  sin(A) = sqrt%281-cos%5E2%28A%29%29 = sqrt%281-%284%2F5%29%5E2%29 = sqrt%281-16%2F25%29 = sqrt%28%2825-16%29%2F25%29 = sqrt%289%2F25%29 = + 3%2F5 = 3%2F5.

    Notice that the sign is "+" for sine, because ∠A is ACUTE.


2.  cos(2A) = cos%5E2%28A%29+-+sin%5E2%28A%29 = %284%2F5%29%5E2 - %283%2F5%29%5E2 = %2816-9%29%2F25 = 7%2F25.


3.  sin(2A) = 2*sin(A)*cos(A) = 2%2A%283%2F5%29%2A%284%2F5%29 = 24%2F25.


4.  tan(2A) = sin%282A%29%2Fcos%282A%29 = %2824%2F25%29%3A%287%2F25%29 = 24%2F7 = 33%2F7.