SOLUTION: Find the exact value of cos θ if the terminal side of θ is standard position contains the point (6,-8).

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Question 42331: Find the exact value of cos θ if the terminal side of θ is standard position contains the point (6,-8).
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!


The coordinates of P are (6,-8).
AO = 6 units and AP = -8 units

From Pythagorus' theorem in rightangled triangle OAP,
OP%5E2=AO%5E2+%2B+AP%5E2
or OP=sqrt%28AO%5E2+%2B+AP%5E2%29
or OP=sqrt%286%5E2+%2B+%28-8%29%5E2%29
or OP=sqrt%2836+%2B+64%29
or OP=sqrt%28100%29
So, OP = 10 units

Now, cos θ = cos(< AOP) = OA%2FOP = 6%2F10 = 3%2F5

Note:
sin θ = sin(< AOP) = AP%2FOP = %28-8%29%2F10 = -4%2F5 and tan θ = tan(< AOP) = AP%2FOA = %28-8%29%2F6 = -4%2F3