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if @ and $ are the acute angles such that sin@=1/2 and cos$=1/3 then @+$ lies in the interval? ans=]pie/3,2pie/3[

if @ and $ are the acute angles such that sin@=1/2 and cos$=1/3 then @+$ lies in the interval?


ans=]pie/3,2pie/3[

Grade:12

1 Answers

Devasish Bindani
45 Points
10 years ago

sin@=1/2 => cos@=31/2

cos$=1/3 =>sin$=(2*21/2)/3

Cos(@+$)=cos@cos$-sin@sin$=(1/31/2-21/2/3)=(1-61/2)/3

the value of 61/2=0.573 and cos (pie/3)=31/2/2=0.868 and cos (2pie/3)=0.5

since value of cos(@+$)lies bettween cos(pie/3) and cos(2pie/3)

thus @+$ lies bettween [pie/3,2pie/3]

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