SOLUTION: Can someone please help me with this question?! Thank you! If sin(alpha)=0.871 and sin(beta)=0.966 with both angles’ terminal rays in Quadrant-I, find the values of tan(alpha +

Algebra ->  Trigonometry-basics -> SOLUTION: Can someone please help me with this question?! Thank you! If sin(alpha)=0.871 and sin(beta)=0.966 with both angles’ terminal rays in Quadrant-I, find the values of tan(alpha +       Log On


   

Question 607040: Can someone please help me with this question?! Thank you!
If sin(alpha)=0.871 and sin(beta)=0.966 with both angles’ terminal rays in Quadrant-I, find the values of tan(alpha + beta). Your answers should be accurate to 4 decimal places.
Answer by lwsshak3(11628) About Me  (Show Source):
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Can someone please help me with this question?! Thank you!
If sin(alpha)=0.871 and sin(beta)=0.966 with both angles’ terminal rays in Quadrant-I, find the values of tan(alpha + beta). Your answers should be accurate to 4 decimal places.
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sin a=.871=opp side/hypotenuse=.871/1
adj side=√(1^-.871^2)=√.2414≈.4913
tan a=opp/adj=.871/.4913≈1.7728
..
sin b=.966=opp side/hypotenuse=.966/1
adj side=√(1^-.966^2)=√.0668≈.2585
tan b=opp side/adj side=.966/.2585≈3.7370
..
Using tan addition formula:
tan(a+b)=(tan a+ tan b)/(1-tan a tan b)
=(1.7728+3.7370)/(1-1.7728*3.7570)
=5.5098/-5.6604=-.9734
tan(a+b)=-.9734 (in quadrant II where tan <0)