SOLUTION: Given that sinx=3/5 and it is in quadrant 1. Find sin2x and cos 2x and tan 2x

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Question 1196984: Given that sinx=3/5 and it is in quadrant 1. Find sin2x and cos 2x and tan 2x
Answer by ikleyn(52880) About Me  (Show Source):
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Given that sinx=3/5 and it is in quadrant 1. Find sin2x and cos 2x and tan 2x
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Step by step 


(a)  If sin(x) = 3/5 and x is in QI, then

        cos(x) = sqrt%281-sin%5E2%28x%29%29 = sqrt%281-%283%2F5%29%5E2%29 = sqrt%281-9%2F25%29%29 = sqrt%2816%2F25%29 = 4%2F5


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


     Part (a) is complete.  From the answer, notice that 2x is in QI.



(b)  cos(2x) = sqrt%281-sin%5E2%282x%29%29 = sqrt%281-%2824%2F25%29%5E2%29 = sqrt%281-576%2F625%29%29 = sqrt%2849%2F625%29 = 7%2F25.    ANSWER



(c)  tan(2x) = sin%282x%29%2Fcos%282x%29 = %28%283%2F5%29%29%2F%28%287%2F25%29%29 = %283%2A25%29%2F%285%2A7%29 = %283%2A5%29%2F7 = 15%2F7.    ANSWER

Solved.     All your questions are answered.