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# Chapter 7 Note

### Chapter 7 Trig notes

Law of Sines -Used to solve non-rt triangles -To find sides: a/sinA=b/sinB=c/sinC -To find Angles: sinA/a=sinB/b=sinC/c
LoS: The Ambiguous Case (Don't make an A.S.S of your self) Only Applies to Angle Side Side case -Possible no solution, 2 solutions, or 1 solution. -To determine: Solve triangle ABC, find < prime (<') of smallest angle. -Angle prime= supplement of <. -If <A + <B + <' is = to 180 then triangle has two solutions.
Law of Cosines Formulas Given 1 side: a^2=b^2+c^2-2bc(cosA) *b^2=a^2+c^2-2ac(cosB) *c^2=a^2+b^2-2ab(cosC)
Area of Triangle (SAS & Area=S) S=1/2bc(sinA) S=1/2ac(sinB) S=1/2ab(sinC)
Area of Triangle (AAS or ASA & Area=S) S=a^2sinBsinC/2sinA S=b^2sinAsinC/2sinB S=c^2sinAsinB/2sinC
Area of Triangle (SSS & Area=S) S=√s(s-a)(s-b)(s-c) where s=a+b+c/2
Vector Addition & Subtraction Vector U+V=< ux+uy,vx+vy> Vector U-V=< ux-uy,vx-vy>
Scalar Multiplication If, Vector U=< ux,uy> and C=scalar (any real #) then, C(U)=C< ux,uy> or < C(ux),C(uy)> -Simply Mult. the cords by the scalar
Magnitude of Vector lCU + CVl=√a^2+b^2
Dot Product U•V=ux(uy)+uy(vy)
Cosine Theorem U•V=lUllVlcosθ also, cosθ=U•V/lUllVl
Created by: ed_delao