# Trig equations

 cos(a+b) cos(a)cos(b) - sin(a)sin(b) cos(a-b) cos(a)cos(b) + sin(a)sin(b) sin(a+b) sin(a)cos(b) + cos(a)sin(b) sin(a-b) sin(a)cos(b) - cos(a)sin(b) tan(a-b) tan(a)-tan(b) / 1+tan(a)tan(b) tan(a+b) tan(a)+tan(b) / 1-tan(a)tan(b) sin2(a) 2sin(a)cos(a)2cos(a)sin(a) cos2(a) •cos^2(a) - sin^2(a) •1 - 2sin^2(a)•2cos^2(a) - 1 tan2(a) 2tan(a) / 1 - tan^2(a) sin(a/2) √[1-cos(a)] / 2 cos(a/2) √[1+cos(a)] / 2 tan(a/2) sin(a)/1+cos(a)1-cos(a)/sin(a)±√[(1-cos(a)/1+cos(a)] Law of Sines sin(A)/a = sin(B)/b = sin(C)/c Law of Cosines a^2 = b^2 + c^2 - 2(a)(b)cos(A) Heron's Fomula (find the area of a triangle given 3 sides) √[s(s-a)(s-b)(s-c)] s= 1/2(a+b+c) What is the magnitude of a vector? The length of the line that is made.V= <4,2>= 4i + 2j Magnitude of a vector |V|= √[a^2 + b^2] <--- Pythagorean theorem With imaginary numbers, the x and y axis become the _____ and ______ axis, respectively. Imaginary and Real When adding two vectors the result r is the line that can be drawn between the endpoints of each vector. Dot Product of two vectors v • w= ac + bd Angle between two vectors cosθ= (u•v)÷(|mag. u|)(|mag. v|) Unit Vector= magnitude of 1 Formula to find unit vector u= / |mag. v| imaginary number i= √[-1] i^2= i^4= -11 trig form of complex number equation z=x + yi z= r(cosθ)+r(sinθ)= r(cosθ+sinθ) For complex numbers: sinθ= cosθ= tanθ= y/r ; y=r(sinθ)x/r ; x=r(cosθ)y/x How do you find r for a complex number equation? Magnitude of z:|z|= √[x^2 + y^2] How is the argument (angle) measured? ALWAYS fromt the positive x-axis. To multiply complex number equations: multiply the modulus (r) and add the argument (the angles on the cosine and sine in the parenthesis). To divide complex number equations: divide the modulus (r) and subtract the argument (the angles on the cosine and sine in the parenthesis). Demovire's theorem (multiplying a complex number equation by itself) z^n= r^n(cos(nθ) + i sin(nθ)) Authortenorsextets ID45322 Card SetTrig equations Descriptionlook at title Updated2010-11-15T16:44:18Z Show Answers