Question 737601
If sin t = 1/3 and pi/2 < t < pi, then determine the exact value of cos t, sin(2pi - t), and cos(2pi - t).
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let O=opposite side
let A=adjacent side
let H=hypotenuse
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sin t=1/3=O/H
O=1, H=3
{{{A=sqrt(H^2-1^2)=sqrt(9-1)=-sqrt(8)}}}
{{{cos(t)=A/H=-sqrt(8)/3=-2sqrt(2)/3}}}
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{{{sin(2pi-t)=-1/3}}} (Note: this moves the standard position of t from Q2 to Q3 where sin<0, with the same reference angle) You could use the sin addition formula to show this.
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{{{cos(2pi-t)=-2sqrt(2)/3}}}(Note: this moves the standard position of t from Q2 to Q3 where cos<0, with the same reference angle) You could use the cos addition formula to show this.