SOLUTION: Find the exact value of the trigonometric function given that: Cos v = -15/17 and sin u = -3/5 5. cos(u+v) 6. tan(v-u) Thank You!

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Question 699490: Find the exact value of the trigonometric function given that: Cos v = -15/17 and sin u = -3/5
5. cos(u+v)
6. tan(v-u)
Thank You!

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Find the exact value of the trigonometric function given that: Cos v = -15/17 and sin u = -3/5
5. cos(u+v)
6. tan(v-u)
..
O=opposite side
A=adjacent side
H=hypotenuse
..
(In quadrant II where cos<0 and sin>0)
cos v=-15/17=A/H
A=-15, H=17
O=√(H^2-A^2)=√(17^2-15^2)=√(289-225)=√64=8
sin v=O/H=8/17
tan v=O/A=-8/15
...
(In quadrant IV where sin<0 and cos>0)
sin u=-3/5=O/H
O=-3, H=5
A=√(H^2-O^2)=√(5^2-3^2)=√(25-9)=√16=4
cos u=A/H=4/5
tan u=O/A=-3/4
..
cos(u+v)=cos u cos v-sin u sin v
=4/5*-15/17+3/5*8/17
=-60/85+24/85
=-36/85
..
tan(v-u)=(tan v-tan u)/(1+tan v*tan u)
=(-8/15+3/4)/(1+8/15*3/4)
=(-32/60+45/60)/1+24/60)
=(13/60)/(84/60)
=13/84