SOLUTION: given that sin(theta) equals (1/5)and that the terminal side is in quadrant I, find exact answers for cos(theta+(pi/4))

Question 851224: given that sin(theta) equals (1/5)and that the terminal side is in quadrant I, find exact answers for cos(theta+(pi/4))
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
given that sin(theta) equals (1/5)and that the terminal side is in quadrant I, find exact answers for cos(theta+(pi/4))
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If sin(t) = 1/5, cos(t) = sqrt(5^2-1^2)/5 = 2sqrt(6)/5
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Then cos(t+(pi/4)] = cos(t)*cos(pi/4)-sin(t)sin(pi/4)
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= (sqrt(2)/2)(cos(t)+sin(t))
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= (sqrt(2))/2)((1/5)+(2sqrt(6)/5]
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= (sqrt(2)/2)(1+2sqrt(6))/5
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= (sqrt(2)+4sqrt(3))/10
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Cheers,
Stan H.
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