Sentence examples for left sin from inspiring English sources
Now, one can show that log {f}_Cleft({Q}_Cleft({F}_Y t)right)right)=- log left(pi theta right)+2 log left( sin left(pi {F}_Y t)right)right). (20).
On using the following series expansion from Gradshteyn and Ryzhik (2007, p. 55) log left( sin left(pi xright)right)= log left(pi xright)+{displaystyle sum_{j=1}^{infty }{V}_j}{x}^{2j}, (21 where ( {V}_j=frac{{left -1right)}^j{V}_j=frac{{left -1right}_{2j}}{2j(2j)!} ) and B j is the Bernoulli number, we get the result in (18).□.
left{begin{array}{l}M{E}_F={displaystyle sum_{i=1}^m{A}_{i,i}left( cos beta {x}_i-D{F}_iright)} {F}_R=lambda left( sin alpha -{displaystyle sum_{i=1}^nD{F}_i{x}_i}right)end{array}right.
The Euler angles θ ∗∈ and ψ ∗∈(−π/2,π/2) are retrieved from the components of the vector (vec {e}^{ast }) since ( vec {e}^{ast } = left (sin theta ^{ast } cos psi ^{ast }, -sin psi ^{ast }, cos theta ^{ast } sin psi ^{ast }right)^{top } ).
We next compute begin{aligned}&(cos t + sin t, lambda _1), (cos t + sin t, lambda _2) &quad = 1 + left( frac{lambda _1+lambda _2}{2} right) ^2 - sin ^2 t, left( frac{lambda _1-lambda _2}{2} right) ^2 &quad quad - left( sin t - cos t, frac{lambda _1+lambda _2}{2} right) ^2 &quad le 1 + frac{H^2}{4}.
sol 1 (a), sol 2 (b) I q)=frac{mathrm{scale}}{V}cdot {left(frac{3Vleft varDelta rho right)left( sin (qR)- qRcos qR right)}{ qR)^3}right)}^2 wherem{b}mathrm{k}mathrm{g} (2)where scale is a volume fraction, V is the volume of the scatterer, R is the radius of the sphere, bkg is the background level, and Δρ is the contrast [21].
Wearing the same sweatshirt covered in his family's painted handprints that he wore at the 2006 tournament, Mr. Einhorn was among the 3,400 competitors leaving Sin City at least $10,000 lighter (the buy-in for the Texas Hold 'Em Championship tournament).
Coulibaly was worried because a friend had told him: "The prophet says you can leave sins behind you but absolutely not debt".
The transmitting power is: {P}_l=frac{V_s{V}_r}{Z_c sin left(beta lright)} sin delta =frac{P_n}{ sin left(beta lright)} sin delta (5).
mathrm{Traffic} mathrm{Rate} = raisebox{1ex}{$1$} left/ raisebox{-1ex raisebox{-1extimes max mathrm{rate}{times left(1+ sin(t)right) (4).
Using the Jacobi identity exp left( jupsilon sin beta right)={displaystyle sum_{nu =-infty}^{+infty }{J}_{nu}left upsilon right)} exp left( jnu beta right) (13).
