Converting these back to real part/imaginary part notation eiπ/4 = cos π 4 isin π 4 = 1 √ 2 i √ 2 and e5iπ/4 = cos 5π 4 isin 5π 4 = − 1 √ 2 − i √ 2 This exercise is part of an interesting subject in mathematics called the nth Solution Set Simple Harmonic Motion Physics 107 Answers Simple Harmonic Motion 1 The maximum displacement from the equilibrium position A = 100 cm The time for one complete oscillation T = π/2 s Notice the maximum positive displacement x = 100 cm occurs at t = 0 and the next time at t = π/2 sSolution sin 2 θ = 3 4 ⇒ sin θ = ± √ 3 2 ⇒ sin θ = sin (± π 3) ⇒ θ = nπ (1) n ∙ (± π 3 ), where, n ∈ Z ⇒ θ = nπ ± π 3, where, n ∈ Z Therefore the general solution of sin 2 θ = 3 4 is θ = nπ ± π 3, where, n ∈ Z Trigonometric Equations General solution of the equation sin x = ½
List Of Trigonometric Identities Wikipedia
