InterviewSolution
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InterviewSolution
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Find the principal solutions of each of the following equations : (i) `sinx=(1)/(2)` (ii) `cosx=(1)/(sqrt(2))` |
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Answer» (i) The given equation is sin `x=(1)/(2)`. We know that `"sin"(pi)/(6)=(1)/(2)andsin(pi-(pi)/(6))=(1)/(2)`. `therefore "sin"(pi)/(6)=(1)/(2)and"sin"(5pi)/(6)=(1)/(2)`. Hence , the principal solutions are `x=(pi)/(6)andx=(5pi)/(6)`. (ii) The given equation is cos x `=(1)/(sqrt(2))`. We know that `"cos"(pi)/(4)=(1)/(sqrt(2))andcos(2pi-(pi)/(4))=(1)/(sqrt(2))`. `therefore"cos"(pi)/(4)=(1)/(sqrt(2))and "cos"(7pi)/(4)=(1)/(sqrt(2))`. Hence , the principal solutions are `x=(pi)/(4)and x = (7pi)/(4)`. (iii) The given equation is tan `x=(1)/(sqrt(3))`. We know that tan `(pi)/(6)=(1)/(sqrt(3))and tan (pi+(pi)/(6))=(1)/(sqrt(3))`. `therefore "tan"(pi)/(6)=(1)/(sqrt(3))and" tan"(7pi)/(6)=(1)/(sqrt(3))`. Hence , the principal solutions are `x=(pi)/(6) andx=(7pi)/(6)`. |
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