SOLUTION: given angle x is in standard position with its terminal arm in quadrant 3 and tanx= 7/5, find exact value of cos2x

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Question 1205224: given angle x is in standard position with its terminal arm in quadrant 3 and tanx= 7/5, find exact value of cos2x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
angle x is in standard position with its terminal arm in quadrant 3+
+tan%28x%29=+7%2F5

tan%28x%29=+opp%2Fadj

opp%2Fadj=7%2F5+=> opp=7, adj=5

then hyp=sqrt%287%5E2%2B5%5E2%29=sqrt%2874%29
since sin%28x%29=opp%2Fhyp and cos%28x%29=adj%2Fhyp, we have


sin%28x%29=7%2Fsqrt%2874%29 and cos%28x%29=5%2Fsqrt%2874%29

since sin%28x%29 and cos%28x%29 are negative in Q III, use

sin%28x%29=-7%2Fsqrt%2874%29 and cos%28x%29=-5%2Fsqrt%2874%29

to find exact value of cos%282x%29, use identity:
cos%282x%29=cos%5E2%28x%29+-+sin%5E2%28x%29
cos%282x%29=%28-5%2Fsqrt%2874%29%29%5E2+-+%28-7%2Fsqrt%2874%29%29%5E2
cos%282x%29=25%2F74+-+49%2F74
cos%282x%29=+-+24%2F74
cos%282x%29=-12%2F37