Question 855428
let theta be angle in quadrant II such that sec(theta)=-10/7. Find the exact values of cot(theta) and sin(theta)
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use x for theta
secx=-10/7
cosx=-7/10
sinx=√(1-cos^2x)=√(1-49/100)=√(51/100)=√51/10
cotx=cosx/sinx=-7/√51=-7√51/51
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calculator check:
cosx=-7/10
x≈134.43˚
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sinx=sin(134.43)≈0.7141
exact value=√51/10≈0.7141
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cotx=cot(134.43)=-0.9803
exact value=-7√51/51≈0.9802