103 trigonometry problems titu andreescu & zuming feng

... θ.ABCDFigure 1.4.Think Within the BoxFor two angles α (Greek “alpha") and β (Greek “beta") with 0◦< α,β,α + β<90◦, it is not difficult to note that the trigonometric functions ... addition and subtraction formulas defined for angles α andβ with 0◦<α,β<90◦and α + β<90◦. Under our general definitions of trigonometry functions, we can expand these formulas to hold for ... triangle ABDis equilateral. Hence, |AD|=|AB| and |AC|=|AD|2. Because ABC is a right4 103 Trigonometry Problems triangle, |AB|2=|AC|2+|BC|2.Sowehave|BC|2=|AB|2−|AB|24=3|AB|24,or...

... Interval Estimationθ1α−$( ; )Uθ ε−∞ +0Uε>$( ) 1UPθ θ ε α−∞ < < + = −θ1α−$( ; )L− +∞θ ε0L>ε$( ) 1LP− < < +∞ = −θ ε θ αPoint Estimation Example ... xµµ1 2,θ θ1 2,t t1 2 1 2( , ) ( )t t t tθ< <1α−$θθ1α−$ $( ; )θ ε θ ε− +0ε>$ $( ) 1Pθ ε θ θ ε α− < < + = −Single Sample: Estimating a Proportion  ... ta được: 24.89 < µ < 27.83 (gam) b) Đây là bài toán ước lượng khối lượng trung bình µB của các sản phẩm loại BSản phẩm loại B: /2 /2s sx z x zn nα αµ− < < +xBi13 17Số...

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