Answers to lab 9/14

sin alpha = 1/10

(1/10)² + cos²alpha = 1
1/100 + cos²alpha = 1 
cos²alpha = 1 - 1/100 = (100-1)/100 = 99/100
sqrt(cos²alpha) = sqrt(99/100) = sqrt(99)/10 = 3sqrt(11)/10
cos alpha = 3sqrt(11)/10
tan alpha = sin/cos = 1/3sqrt(11) = sqrt(11)/33

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cos beta = 5/7


sin²beta + (5/7)² = 1

sin²beta + 25/49 = 1
sin²beta = 1 - 25/49 = (49-25)/49 = 24/49
sin beta = sqrt(24/49)

sin beta = sqrt(24)/7 = 2sqrt(6)/7
tan beta = sin/cos = 2sqrt(6)/5

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tan theta = 3
3²cos theta + cos² theta = 1
9cos² theta + cos² theta = 1
10cos² theta = 1

cos² theta = 1/10
cos theta = sqrt(1/10) = sqrt(10)/10
sin theta = tan theta cos theta = 3sqrt(10)/10


Don't worry if I didn't get around to correcting yours personally.  Everyone who was in class gets credit for the lab.