Question 931633: Find the exact value under the given conditions.
cos a = 1/3 , 0 < a < pi/2. sin b= -1/2 , -pi/2 < b < 0
Find tan ( a + b)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the exact value under the given conditions.
cos a = 1/3 , 0 < a < pi/2. sin b= -1/2 , -pi/2 < b < 0
Find tan ( a + b)
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reference angle a is in quadrant I where sin>0, cos>0
reference angle b is in quadrant IV where sin<0, cos>0
..
cosa=1/3
sina=√(1-cos^2(a))=√(1-(1/9))=√(8/9)=√8/3
..
sinb=-1/2
cosb=√(1-sin^2(b))=√(1-(1/4))=√(3/4)=√3/2
..
tana=√8/1=√8
tanb=-1/√3=-√3/3
tan(a+b)=(tana+tanb)/(1-tana*tanb)=(√8-√3/3)/(1-(√8*-√3/3))
=(3√8-√3)/3)/(3+(√24)/3=(3√8-√3)/(3+√24)
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