# SOLUTION: find the exact value given the following conditions a. cos (a + b) b. sin (a + b) c. tan (a + b) sin a = 5/6, pi/2 < a < pi, and tan b = 3/7, pi < b < 3pi/2

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: find the exact value given the following conditions a. cos (a + b) b. sin (a + b) c. tan (a + b) sin a = 5/6, pi/2 < a < pi, and tan b = 3/7, pi < b < 3pi/2      Log On

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Question 633150: find the exact value given the following conditions a. cos (a + b) b. sin (a + b) c. tan (a + b) sin a = 5/6, pi/2 < a < pi, and tan b = 3/7, pi < b < 3pi/2Answer by lwsshak3(6469)   (Show Source): You can put this solution on YOUR website!find the exact value given the following conditions a. cos (a + b) b. sin (a + b) c. tan (a + b) sin a = 5/6, pi/2 < a < pi, and tan b = 3/7, pi < b < 3pi/2 ** O=opposite side A=adjacent side H=hypotenuse .. a is a reference angle in quadrant II where sin>0 and cos<0 sin a=5/6=O/H (given) A=√(H^2-O^2)=√(36-25)=√11 cos a=-√11/6 tan a=-5/√11 .. b is a reference angle in quadrant III where both sin and cos<0 tan b=3/7=O/A (given) H=√(O^2+A^2)=√(9+49)=√58 sin b=–3/√58 cos b=–7/√58 .. a. cos (a + b) =cos a*cos b-sin a*sin b =[-√11/6*-7/√58]-[(5/6)*(-3√58)]=(7√11+15)/(6√58) .. b. sin (a + b) =sin a*cos b+cos a*sin b =[(5/6)*(-7/√58)+[(-√11/6)*(-3/√58)] =(-35+3√11)/(6√58) .. tan(a + b) =(tan a+tan b)/(1-tan a tan b) =[(-5/√11)+(3/7)]/[1-(-5/√11)(3/7)]