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Home Trigonometric Functions Derivatives of Trigonometric Functions Theorem 4: Integrals of Trigonometric Functions
 
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Theorem 4: Integrals of Trigonometric Functions

THEOREM 4

(i)

∫ cos θ dθ = sin θ + C,

∫ sin θ dθ = -cos θ + C.

(ii)

∫ sec2 θ dθ = tan θ + C,

∫ esc2 θ dθ = -cot θ + C.

(iii)

∫ sec θ tan θ dθ = sec θ + C,

∫ csc θ cot θ dθ = -csc θ + C.

At time t, θ has the value θ = ωt. So the motion of the particle is given by the parametric equations

x = r0 cos (cot), y = r0 sin (cot).

The shadow is directly below the particle, and its position is given by the x-component

x = r0 cos (cot).

The velocity and acceleration of the shadow are

07_trigonometric_functions-79.gif
Home Trigonometric Functions Derivatives of Trigonometric Functions Theorem 4: Integrals of Trigonometric Functions

Last Update: 2006-11-06