What is e^{-t}sin(sqrt(3t)) ?

The solution to e^{-t}sin(sqrt(3t)) is (sin(sqrt(3)sqrt(t)))/(e^t)

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simplify e^{-t}sin(sqrt(3t))

simplify

e^{- t} sin (3 t)

\frac{sin ( 3 t )}{e ^{t}}

Solution steps

e^{- t} sin (3 t)

Apply exponent rule:

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

= \frac{1}{e ^{t}} sin (3 t)

3 t = 3 t

= \frac{1}{e ^{t}} sin (3 t)

Multiply fractions:

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

= \frac{1 \cdot sin ( 3 t )}{e ^{t}}

Multiply:

1 \cdot sin (3 t) = sin (3 t)

= \frac{sin ( 3 t )}{e ^{t}}

5.28 \cdot 1 0^{- 6}

(\frac{1}{e ^{2 t}})^{- 1}

- e^{- e^{0}}

k (e^{k t})^{2}

124 e^{- 0.0077 (65)}

What is e^{-t}sin(sqrt(3t)) ?
The solution to e^{-t}sin(sqrt(3t)) is (sin(sqrt(3)sqrt(t)))/(e^t)