SOLUTION: Find the exact value of each of the following under the given conditions: {{{cotA= -24/7}}} {{{pi/2 < A < pi}}} {{{cosB= 5/6}}} {{{0 < B < pi/2 }}} {{{sin (A+B)}}} {{{cos (A-B

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of each of the following under the given conditions: {{{cotA= -24/7}}} {{{pi/2 < A < pi}}} {{{cosB= 5/6}}} {{{0 < B < pi/2 }}} {{{sin (A+B)}}} {{{cos (A-B      Log On


   

Question 719857: Find the exact value of each of the following under the given conditions:
cotA=+-24%2F7 pi%2F2+%3C+A+%3C+pi cosB=+5%2F6 0+%3C+B+%3C+pi%2F2+
sin+%28A%2BB%29
cos+%28A-B%29
sin+%28A-B%29
tan+%28A%2BB%29+
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of each of the following under the given conditions:
cotA=+-24%2F7 pi%2F2+%3C+A+%3C+pi cosB=+5%2F6 0+%3C+B+%3C+pi%2F2+
sin+%28A%2BB%29
cos+%28A-B%29
sin+%28A-B%29
tan+%28A%2BB%29+
***
let o=opposite side
let a=adjacent side
let h=hypotenuse
..
π/2 < A < π (quadrant II)
cotA=-24/7=a/o
a=-24, o=7
h=√(o^2+24^2)=√(49+576)=√625=25
sinA=o/h=7/25
cosA=a/h=-24/25
tanA=o/a=-7/24
...
0 < B < π/2 (quadrant I)
cosB=5/6=a/h
a=5, h=6
o=√(h^2-a^2)=√(36-25)=√11
sinB=o/h=√11/6
cosB=a/h=5/6
tanB=o/a=√11/5
...
Identity: sin(A+B)=sinAcosB+cosAsinB
=7/25*5/6+(-24/25*√11/6)
=35/150-24√11/150=(35-24√11)/150
...
Identity: sin(A-B)=sinAcosB-cosAsinB
=7/25*5/6-(-24/25*√11/6)
=35/150+24√11/150
=(35+24√11)/150
...
Identity:cos(A-B)=cosAcosB+sinAsinB
=-24/25*5/6+7/25*√11/6
=-120/150+7√11/150
=-120+7√11/150
...
Identity:tan(A+B)=(tanA+tanB)/(1-tanAtanB)
=(-7/24+√11/5)/(1-(-7/24*√11/5)
=(-7/24+√11/5)/(1+7√11/120)