Engineering Mechanics

Chapter 1 : Introduction 9

sin^2 θ + cos^2 θ = 1

1 + tan^2 θ = sec^2 θ

1 + cot^2 θ = cosec^2 θ

sin^2 1– cos2
2

A A=

cos^2 1cos2
2

A A

+ =

2 cos A sin B = sin (A + B) – sin ( A – B)

Rules for the change of trigonometrical ratios:

sin (– ) – sin cos (– ) cos tan (– ) – tan () cot (– ) – cot sec (– ) sec cosec (– ) – cosec

A

⎧ θ=θ ⎪ θ=θ ⎪ ⎪⎪ θ=θ ⎨ ⎪ θ=θ ⎪ θ=θ ⎪ ⎪⎩ θ= θ sin (90 – ) cos cos (90 – ) sin tan (90 – ) cot () cot (90 – ) tan sec (90 – ) cosec cosec (90 – ) sec

B

⎧ °θ = θ ⎪ °θ = θ ⎪ ⎪⎪ °θ = θ ⎨ ⎪ °θ = θ ⎪ °θ = θ ⎪ ⎪⎩ °θ= θ

sin (90 ) cos cos (90 ) – sin tan (90 ) – cot () cot (90 ) – tan sec (90 ) – cosec cosec (90 ) sec

C

⎧ °+θ = θ ⎪ °+θ = θ ⎪ ⎪⎪ °+θ = θ ⎨ ⎪ °+θ = θ ⎪ °+θ = θ ⎪ ⎪⎩ °+θ = θ

sin (180 – ) sin cos (180 – ) – cos tan (180 – ) – tan () cot (180 – ) – cot sec (180 – ) – sec cosec (180 – ) cosec

D

⎧ °θ = θ ⎪ °θ = θ ⎪ ⎪⎪ °θ = θ ⎨ ⎪ °θ = θ ⎪ °θ = θ ⎪ ⎪⎩ °θ= θ sin (180 ) – sin cos (180 ) – cos tan (180 ) tan () cot (180 ) cot sec (180 ) – sec cosec (180 ) – cosec

E

⎧ °+θ = θ ⎪ °+θ = θ ⎪ ⎪⎪ °+θ = θ ⎨ ⎪ °+θ = θ ⎪ °+θ = θ ⎪ ⎪⎩ °+θ = θ

Engineering Mechanics

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