SOLUTION: let cos A = -5/13 with A in Q2 and sin B= 3/5 with B in Q1 Find 1. CSC(A-B) 2. TAN(A+B) 3. SEC(A+B) 4. In what Q does (A+B) terminate?

Algebra ->  Trigonometry-basics -> SOLUTION: let cos A = -5/13 with A in Q2 and sin B= 3/5 with B in Q1 Find 1. CSC(A-B) 2. TAN(A+B) 3. SEC(A+B) 4. In what Q does (A+B) terminate?      Log On


   

Question 845900: let cos A = -5/13 with A in Q2 and sin B= 3/5 with B in Q1
Find 1. CSC(A-B) 2. TAN(A+B) 3. SEC(A+B) 4. In what Q does (A+B) terminate?
Answer by lwsshak3(11628) About Me  (Show Source):
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let cos A = -5/13 with A in Q2 and sin B= 3/5 with B in Q1
Find 1. CSC(A-B) 2. TAN(A+B) 3. SEC(A+B) 4. In what Q does (A+B) terminate?
***
cos A=-5/13
sin A=12/13
..
sin B=3/5
cos B=4/5
..
1. csc (A-B)=1/sin(A-B)
sin(A-B)=sin A*cos B-cos A*sinB=12/13*4/5(-(-5/13)*3/5)=48/65+15/65=63/65
csc(A-B)=65/63
..
3.sec (A+B)=1/cos(A+B)
cos(A+B)=cos A*cos B+sin A*sinB=-5/13*4/5-12/13*3/5)=-20/65-36/65=-56/65
sec(A+B)=-65/56
..
2. tan(A+B)=sin(A+B)/cos(A+B)
sin(A+B)=sin A*cos B+cos A*sinB=12/13*4/5+(-5/13)*3/5)=48/65-15/65=33/65
tan(A+B)=-33/56
..
4. cos A=-5/13 (in Q2)
A≈112.62
sin B=3/5
B≈36.87˚
A+B≈149.49˚
A+B terminates in quadrant II
..
A-B≈75.75
calculator check:
sin(A-B)≈sin(75.75)≈0.9692
exact value=63/65≈0.9692
..
sin(A+B)≈sin(149.49)≈0.5077
exact value=33/65≈0.5077
..
cos(A+B)≈cos(149.49)≈-0.8615
exact value=-56/65≈-0.8615
..
tan(A+B)=tan(149.49)=-0.5892
exact value=-33/56≈-0.5892