SOLUTION: Suppose cos(t)=-1/3 and sin(t)<0 Use appropriate identities to find each of the following?
sec(-1)
sin(-t)
cos(t+5π/3)
sin(2t)
Please give details I have to u
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Question 924929: Suppose cos(t)=-1/3 and sin(t)<0 Use appropriate identities to find each of the following?
sec(-1)
sin(-t)
cos(t+5π/3)
sin(2t)
Please give details I have to understand
Thanks!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Suppose cos(t)=-1/3 and sin(t)<0 Use appropriate identities to find each of the following?
sec(-1)
sin(-t)
cos(t+5π/3)
sin(2t)
***
cos(t)=-1/3
sin(t)<0
reference angle t is in quadrant III where sin<0, cos<0
sin(t)=-√(1-cos^2(t))=-√(1-1/9)=-√(8/9)=-√8/3
..
sec(-1)=1/cos(-1)=1/-0.54≈-1.85
note:(reference angle=1(radian) in quadrant IV where sin<0)
sin(-t)=-sin(t)=-√8/3
cos(t+5π/3)=cos(t)*cos(5π/3)-sin(t)*sin(5π/3)
=-1/3*1/2-(-√8/3)*(-√3/2)=-1/6-√24/6=-(1+√24)/6
..
sin(2t)=2*sin(t)*cos(t)=2*-√8/3*-1/3=2√8/9
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