SOLUTION: If tan(theta)= (sqrt5/2), and pi <0<(3pi/2) what are the exact values of cos(theta), sin(theta) and cot(theta) No inverse trig functions.

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Question 745763: If tan(theta)= (sqrt5/2), and pi <0<(3pi/2) what are the exact values of cos(theta), sin(theta) and cot(theta) No inverse trig functions.
Answer by lwsshak3(11628) About Me  (Show Source):
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If tan(theta)= (sqrt5/2), and pi <0<(3pi/2) what are the exact values of cos(theta), sin(theta) and cot(theta) No inverse trig functions.
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tan%28x%29=sqrt%285%29%2F2 (in quadrant III)
opposite side=-√5
adjacent side=-2
hypotenuse=√(2^2+√5^2)=√(4+5)=√9=3
cos(x)=-2/3
sin(x)=-√5/3
cot(x)=-2/-√5=(2√5)/5
..
Check: (with calculator)
tan(x)=√5/2 (in quadrant III)
x≈228.1897º
cos(x)=cos(228.1897º)≈-0.6666..
exact value=-2/3≈-0.6666..
..
sin(x)=sin(228.1897º)≈-0.7454..
exact value=-√5/3≈-0.7454..
..
cot(x)=cot(228.1897º)≈0.8944..
exact value=5√5/3≈0.8944..