Applied Mechanics and Graphic Statics
The resolved part of the resultant of two forces inclined at an angle θ in a given direction is

Arithmetical sum of the resolved parts of the forces in the direction
Algebraic sum of the resolved parts of the forces in the direction
Sum of the forces multiplied by the tangent θ°
Difference of the forces multiplied by cosine θ°

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Applied Mechanics and Graphic Statics
‘ω’ rad/sec is the angular velocity of a crank whose radius is ‘r’. If it makes θ° with inner dead centre and obliquity of the connecting rod ‘l’ is ‘ϕ’, the velocity v of the piston, is given by the equation

ω (l sin ϕ + r cos ϕ tan θ)
ω² (l sin ϕ - r cos θ tan ϕ)
ω² (l sin ϕ + r cos φ tan θ)
ω² (l cos ϕ + r sin ϕ tan θ)

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Applied Mechanics and Graphic Statics
Lami's theorem states that

Three coplanar forces acting at a point will be in equilibrium if each force is inversely proportional to the sine of the angle between the other two
Three forces acting at a point are always in equilibrium
If three forces acting on a point can be represented in magnitude and direction by the sides of a triangle, the point will be in the state of equilibrium
Three coplanar forces acting at a point will be in equilibrium, if each force is proportional to the sine of the angle between the other two

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