Use a double angle identity and then factor to solve the equation in the interva

Question

Use a double angle identity and then factor to solve the equation in the interval (0,2 pi). (Enter your answer as a comma-separated list). Sin 2 theta + sin theta = 0 Use a graphing device to find the solution of the equation, correct to two decimal places. (Enter your answers as a comma- separated list). Sin 2x = x The displacement of a spring vibrating in damped harmonic motion is given by the following equation. Find the first four times when the spring is at its equilibrium position, y = 0, and starting at time t = 0. (Enter your answers as a comma-separated list.) y = 4 e^-7t sin 2 pi t

Explanation / Answer

1) sin2 theta+sintheta=0

2sinthetacostheta+sintheta =0

sintheta(2costheta+1) =0

sintheta=0 and cos theta =-1/2

theta = 0, pi,     theta = 2pi/3 , 4pi/3

2) by using graphing divice x= sin2x

x-sin2x=0 we will get   x= -0.948   and x=0

3)

y = 4^(-7t) * sin(2t)
so if we set y = 0

4^(-7t) = 0 ----> no solution
or
sin(2t) = 0
2t = 0 or 2t = or 2t = 2 or ..
t = 0 or t = 1/2 or t = 1 or t= ..
looks like every half second, starting with t = 0

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