SOLUTION: Suppose sin(u)= -2/9 and tan(u)<0 a. locate the terminal point P_u for u on the unit circle and find its coordinates b. Find the exact value of each of the following: i. cos

Question 959837: Suppose sin(u)= -2/9 and tan(u)<0
a. locate the terminal point P_u for u on the unit circle and find its coordinates
b. Find the exact value of each of the following:
i. cos(74π-u)
ii. tan(u+3π/2)
iii. csc(-u)
Thank you
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Suppose sin(u)= -2/9 and tan(u)<0
reference angle (u) is in quadrant IV
adjacent side of reference right triangle in quadrant IV=√(9^2)-(2^2)=√(81-4)=√77
cos(u)=√77/9
tan(u)=sin(u)/cos(u)=-2/√77
a. locate the terminal point P_u for u on the unit circle and find its coordinates
terminal point P on the unit circle =(√77/9,-2/9)
b. Find the exact value of each of the following:
i. cos(74π-u)=cos(74π)*cos(u)+sin(74π)*sin(u)=1*√77/9+0*-2/9=√77/9
ii. tan(u+3π/2)=(tan(u)+tan(3π/2))/(1-tan(u)*tan(3π/2))=-2/√77+u.d./1-2/√77*u.d.=undefined
iii. csc(-u) =1/sin(-u)=1/-sin(u)=9/2
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