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Popular >

simplify e^{-at}cos(ωt+θ)

Solution

simplify

e^{- a t} cos (ω t + θ)

Solution

\frac{cos ( ω t + θ )}{e ^{a t}}

Solution steps

e^{- a t} cos (ω t + θ)

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{a t}} cos (ω t + θ)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot cos ( ω t + θ )}{e ^{a t}}

Multiply:

1 \cdot cos (ω t + θ) = cos (ω t + θ)

= \frac{cos ( ω t + θ )}{e ^{a t}}

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Frequently Asked Questions (FAQ)

What is e^{-at}cos(ωt+θ) ?
The solution to e^{-at}cos(ωt+θ) is (cos(ωt+θ))/(e^{at)}