SOLUTION: Given that tan(θ)=3/4 and θE(π,3π/2); find the values of the remaining five trigonometric functions of θ

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Question 143017: Given that tan(θ)=3/4 and θE(π,3π/2); find the values of the remaining five trigonometric functions of θ
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Given that tan(θ)=3/4 and θE(π,3π/2); find the values of the remaining five trigonometric functions of θ
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If tan(theta) is 3/4, theta is in the 3rd quadrant where x= -4 and y =-3
because tan(theta) = y/x
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r = sqrt(x^2+y^2) = sqrt(3^2+4^2)= 5
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sin(theta) = y/r = -3/5
cos(theta) = x/r = -4/5
tan(theta) = y/x = -3/-4 = 3/4
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csc(theta) = r/x = -5/3
sec(theta) = r/y = -5/4
cot(theta) = x/y = -4/-3 = 4/3
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Cheers,
Stan H.