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solvefor t,A(-sin(wt+d)w)=0

Solution

solve for

t, A (- sin (wt + d) w) = 0

Solution

t = \frac{2 πn}{w} - \frac{d}{w}, t = \frac{π}{w} + \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

Solution steps

A (- sin (wt + d) w) = 0

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

- sin (wt + d) w = 0

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

sin (wt + d) = 0

General solutions for

sin (wt + d) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

wt + d = 0 + 2 πn, wt + d = π + 2 πn

wt + d = 0 + 2 πn, wt + d = π + 2 πn

Solve

wt + d = 0 + 2 πn : t = \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

wt + d = 0 + 2 πn

0 + 2 πn = 2 πn

wt + d = 2 πn

Move

d

to the right side

wt + d = 2 πn

Subtract

d

from both sides

wt + d - d = 2 πn - d

Simplify

wt = 2 πn - d

wt = 2 πn - d

Divide both sides by

w; w \neq = 0

wt = 2 πn - d

Divide both sides by

w; w \neq = 0

\frac{wt}{w} = \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

Simplify

t = \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

t = \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

Solve

wt + d = π + 2 πn : t = \frac{π}{w} + \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

wt + d = π + 2 πn

Move

d

to the right side

wt + d = π + 2 πn

Subtract

d

from both sides

wt + d - d = π + 2 πn - d

Simplify

wt = π + 2 πn - d

wt = π + 2 πn - d

Divide both sides by

w; w \neq = 0

wt = π + 2 πn - d

Divide both sides by

w; w \neq = 0

\frac{wt}{w} = \frac{π}{w} + \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

Simplify

t = \frac{π}{w} + \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

t = \frac{π}{w} + \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

t = \frac{2 πn}{w} - \frac{d}{w}, t = \frac{π}{w} + \frac{2 πn}{w} - \frac{d}{w}; w \neq = 0

Graph

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