sin²θ + cos²θ = 1 ∫(dx/x) = ln|x| + C sin x = Σ (-1)ⁿ x⁽²ⁿ⁺¹⁾/(2n+1)! sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) v² = u² + 2as C(n, r) = n!/(r!(n-r)!) ΔT_f = iK_fm m = (y₂ - y₁)/(x₂ - x₁) d/dx(e^x) = e^x K_c = ([C]^c[D]^d)/([A]^a[B]^b) P_solution = X_solvent × P^°_solvent Q = It F_x + F_y(dy/dx) = 0 E = E° - (0.0591/n) log Q f(x) = Σ_n=0∞ (f⁽ⁿ⁾(0)/n!)xⁿ e = (v₂ - v₁)/(u₁ - u₂) log_b a = ln a/ln b d/dx(sin x) = cos x T = 2π√(L/g) c = λf d/dx(cos x) = -sin x P = IV s = ut + ½at² α + β = -b/a a_n = a + (n - 1)d

(a+b)ⁿ = Σ_k=0ⁿ (nCk)a^n-kb^k V = L(dI/dt) ∫ u dv = uv - ∫ v du ε = -dΦ/dt E = VIt Percent Purity = (mass of pure substance/mass of sample) × 100 n = c/v cos²(θ/2) = (1 + cosθ)/2 I = ½ Σ c_i z_i² n = mass/M K.E. = ½mv² 2 sin A cos B = sin(A+B) + sin(A-B) (x-h)² + (y-k)² = r² S = a/(1 - r) f'(a) = lim_h→0 (f(a+h)-f(a))/h Normality = Molarity × n Φ = BA cosθ d/dx(ln x) = 1/x cos x = Σ (-1)ⁿ x⁽²ⁿ⁾/(2n)! f''(x) d = |Ax₀ + By₀ + C|/√(A²+B²) Rate = k[A]^m[B]ⁿ U = mgh (Σ a_i²)(Σ b_i²) ≥ (Σ a_ib_i)² y - y₁ = m(x - x₁)

ΔT_b = iK_bm αβ = c/a V = IR n₁ sinθ₁ = n₂ sinθ₂ d = √((x₂-x₁)²+(y₂-y₁)²) F_c = mv²/r lim_x→a f(x)/g(x) = lim_x→a f'(x)/g'(x) f(x) = Σ_n=0∞ (f⁽ⁿ⁾(a)/n!)(x-a)ⁿ P(n, r) = n!/(n-r)! 1/f = 1/v + 1/u p = mv x = [-b ± √(b² - 4ac)]/(2a) cos 2θ = cos²θ - sin²θ V = (4/3)πr³ A = ∫_a^b f(x) dx M = moles/volume pH = -log[H⁺] E = hf s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)) A = ½ab sin C A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| sin 2θ = 2 sinθ cosθ P = W/t ln(P₂/P₁) = -ΔH_vap/R (1/T₂ - 1/T₁) (1+x)ⁿ = Σ ⁿ C _k.x^k

F = ma a_c = v²/r F = k( q₁q₂ )/r² S_n = a(1 - rⁿ)/(1 - r) Equivalent Weight = Molecular Weight/n A = πab sin²(θ/2) = (1 - cosθ)/2 ΔG = ΔH - TΔS π = MRT A = ab sinθ m = f'(x) (f(g(x)))' = f'(g(x))⋅g'(x) S_n = (n/2)[2a + (n - 1)d] x = a sinθ v = u + at A = Pe^rt pK_a = -log K_a e^x = Σ xⁿ/n! a_n = ar^{n - 1} F = q(E + v × B) λ = h/p W = Fd cosθ