SOLUTION: find the exact value of each. a. cos(theta)/2 if sin(theta)=12/13 and 0<theta<90degrees b. sin[cos^-1(0) - sin^-1(1/2)]

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: find the exact value of each. a. cos(theta)/2 if sin(theta)=12/13 and 0<theta<90degrees b. sin[cos^-1(0) - sin^-1(1/2)]      Log On

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Question 101199: find the exact value of each.
a. cos(theta)/2 if sin(theta)=12/13 and 0
b. sin[cos^-1(0) - sin^-1(1/2)]
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
a. cos(theta)/2 if sin(theta) = 12/13 and 0 < theta < 90 degrees
cos(theta)^2 = 1 - sin(theta)^2
cos(theta) = sqrt( 1 - sin(theta)^2 )
cos(theta) = sqrt( 1 - (12/13)^2 ) or cos(theta) = sqrt( 1 - 0^2 )
cos(theta) = sqrt( 25/169 ) or cos(theta) = sqrt( 1 )
cos(theta) = 5/13 or cos(theta) = 1 *cos(theta) = 1 for theta = 0 ~ Cancel
cos(theta)/2 = 5/26

b. sin[cos^-1(0) - sin^-1(1/2)]
sin[pi/2 - pi/6]
sin[pi/3]
sqrt(3)/2