Hey, there! I am not sure if the answers to my questions are right...I picked 1) 253/325, 2) 171/140 & 3) 16/63...If you could tell me what answers you got and how you got them, that would be great! Also, please let me know if my answers are right or wrong. Thank you! :)
1) Suppose sin A = 12/13 with 90º≤A≤180º. Suppose also that sin B = -7/25 with -90º≤B≤0º. Find tan (A – B).
Let sin A = 12/13 with 90º≤A≤180º and tan B = -4/3 with 270º≤B≤360º. Find tan (A + B).
A) -65/56
B) -63/65
C) 16/63
D) 56/33
+23254 Question #1: sin(A) = 12/13 in quadrant 2 sin(B) = -7/25 in quadrant 4
Since A is in Q2, the missing side is -5 and cos(A) = -5/13 and tan(A) = -12/5
Since B is in Q4, the missing side is 24 and cos(B) = 24/13 and tan(B) = -7/24
tan(A-B) = (tan(A) - tan(B) / (1 + tan(A)tan(B))
= (-12/5 - -7/24) / (1 + (-12/5)(-7/24)) = -253/204
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Question #2: cos(A) = 12/13 in quadrant 1 sin(B) = 8/17 in quadrant 2
Since A is in Q1, the missing side is 5 and sin(A) = 5/13 and tan(A) = 5/12
Since B is in Q2, the missing side is 15 and cos(B) = -15/17 and tan(B) = -8/15
tan(A+B) = (tan(A) + tan(B) / (1 - tan(A)tan(B))
= (5/12 + -8/15) / (1 - (5/12)(-8/15)) = -21/220
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Question #3: sin(A) = 12/13 in quadrant 2 tan(B) = -4/3 in quadrant 4
Since A is in Q2, the missing side is -5 and cos(A) = -5/13 and tan(A) = -12/5
tan(A+B) = (tan(A) + tan(B) / (1 - tan(A)tan(B))
= (-12/5 + -4/3) / (1 - (-12/5)(-4/3)) = 56/33
+23254 Question #1: sin(A) = 12/13 in quadrant 2 sin(B) = -7/25 in quadrant 4
Since A is in Q2, the missing side is -5 and cos(A) = -5/13 and tan(A) = -12/5
Since B is in Q4, the missing side is 24 and cos(B) = 24/13 and tan(B) = -7/24
tan(A-B) = (tan(A) - tan(B) / (1 + tan(A)tan(B))
= (-12/5 - -7/24) / (1 + (-12/5)(-7/24)) = -253/204
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Question #2: cos(A) = 12/13 in quadrant 1 sin(B) = 8/17 in quadrant 2
Since A is in Q1, the missing side is 5 and sin(A) = 5/13 and tan(A) = 5/12
Since B is in Q2, the missing side is 15 and cos(B) = -15/17 and tan(B) = -8/15
tan(A+B) = (tan(A) + tan(B) / (1 - tan(A)tan(B))
= (5/12 + -8/15) / (1 - (5/12)(-8/15)) = -21/220
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Question #3: sin(A) = 12/13 in quadrant 2 tan(B) = -4/3 in quadrant 4
Since A is in Q2, the missing side is -5 and cos(A) = -5/13 and tan(A) = -12/5
tan(A+B) = (tan(A) + tan(B) / (1 - tan(A)tan(B))
= (-12/5 + -4/3) / (1 - (-12/5)(-4/3)) = 56/33
