The displacement, y of a mass attached to a spring is modeled by this equation in cosine, where t is the time in seconds. Which expression represents the displacement using only the sine function?
y(t) = 9.6cos(2pi/6(t) - pi/2)
cos (a-b) = cos a cos b + sin a sin b
you know cos pi/2 = 0. keep that in mind and sin pi/2 = 1
cos(2pi/6(t) - pi/2) = cos 2 pi/6t cos pi/2 + sin 2 pi/6 t sin pi/2
oh look
cos 2 pi/6t * 0 + sin 2 pi/6 t *1
remarkable
y(t) = 6sin(pi/6(t)
y(t) = 9.6sin(2pi(t))
y(t) = 9.6sin(2pi/6(t))
y(t) = 6sin(2pi/6(t))
is it A?
Would it be C?
yes
To represent the displacement using only the sine function, we can use one of the trigonometric identities:
sin(x) = cos(x - pi/2)
Using this identity, we can modify the given equation:
y(t) = 9.6cos(2pi/6(t) - pi/2)
= 9.6sin(2pi/6(t))
Therefore, the expression representing the displacement using only the sine function is:
y(t) = 9.6sin(2pi/6(t))