# Statics-Math - Statics(ENGR 2214 Prof S Nasseri What you...

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Unformatted text preview: Statics (ENGR 2214) Prof. S. Nasseri What you need to know from Math! GEN 240 Statics (ENGR 2214) Prof. S. Nasseri Part 1 Preliminary (Algebra, Geometry, Trigonometry) Statics (ENGR 2214) Prof. S. Nasseri Pythagorean Theorem 2 2 2 sin b sin , cos , tan = cos a a b c b a c c θ θ θ θ θ + = = = = a b c θ sin cos tan 1-1 ∞ 1 ∞-1-∞ sin cos Statics (ENGR 2214) Prof. S. Nasseri Pythagorean Theorem hypotenuse Statics (ENGR 2214) Prof. S. Nasseri Pythagorean Theorem 2 2 Law of sines: sin sin sin Law of cosines: 2 cos a b c c a b ab α β γ γ = = = +- a b c β α γ a b c γ Statics (ENGR 2214) Prof. S. Nasseri The unit circle and trigonometric functions sin( ) sin , cos( ) cos , tan( ) tan sin(180 ) sin , cos(180 ) cos , tan(180 ) tan sin(180 ) (4th quadrant) (2nd quadrant) (3rd q sin , cos(180 ) cos , tan(180 ) tan uadrant θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ- = -- =- = -- =- = -- = - + = - + = - + = sin(90 ) cos , cos(90 ) sin s ) (1st quadrant) (2nd quadr in(90 ) cos , cos an (90 ) sin t) θ θ θ θ θ θ θ θ- =- = + = + = - + + +---- + cos sin Statics (ENGR 2214) Prof. S. Nasseri Double- & two-angle relations 2 2 2 2 2 sin(2 ) 2sin cos cos(2 ) 1 cos(2 ) cos sin 2cos 1 so: cos 2 2 tan tan(2 ) 1 tan θ θ θ θ θ θ θ θ θ θ θ θ = + =- =- = =- Two angle relations: Double angle relations: ( 29 ( 29 ( 29 sin sin cos cos sin cos cos cos sin sin tan tan tan 1 tan tan α β α β α β α β α β α β α β α β α β ± = ± ± = ± ± = m m Statics (ENGR 2214) Prof. S. Nasseri Arcs and sectors 2 2 Arc Length, Angle measured in radians, / = arc length/radius 1 Sector area = 2 2 s r s r r r θ θ θ π θ π = = = r s θ Statics (ENGR 2214) Prof. S. Nasseri Similar triangles The sides of two similar triangles are proportional and the angels are the same . The respective heights of these triangles are also proportional to the sides....
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Statics-Math - Statics(ENGR 2214 Prof S Nasseri What you...

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