Find the amplitude, period and phase shift of $y = - 2 \sin \left( 2 x - \frac { 3 } { 2 } \right)$

A)amplitude: $2$, period: $\pi$, phase shift: $3 / 4$

B)amplitude: $- 2$, period: $\pi$, phase shift: $3 / 2$

C)amplitude: $4$, period: $2 \pi$, phase shift: $1$

D)amplitude: $- 2$, period: $4 \pi$, phase shift: $3 / 4$

E) amplitude: $1 / 2$, period: $\pi$, phase shift: $3 / 4$

Question

Find the amplitude, period and phase shift of $y = - 2 \sin \left( 2 x - \frac { 3 } { 2 } \right)$

A)amplitude: $2$, period: $\pi$, phase shift: $3 / 4$

B)amplitude: $- 2$, period: $\pi$, phase shift: $3 / 2$

C)amplitude: $4$, period: $2 \pi$, phase shift: $1$

D)amplitude: $- 2$, period: $4 \pi$, phase shift: $3 / 4$

E) amplitude: $1 / 2$, period: $\pi$, phase shift: $3 / 4$

Quizplus · Accepted Answer

The general equation for a sinusoidal function of the form $y = a \sin ( b ( x - h ) ) + k$ is:
- Amplitude = |a|
- Period = $\frac { 2 \pi } { | b | }$
- Phase shift = h
Comparing this with the given equation, we get:
- Amplitude = |-2| = 2
- Period = $\frac { 2 \pi } { |2| }$ = $\pi$
- Phase shift = $\frac { 3 } { 2 }$ is equivalent to $\frac { 3 } { 2 } - \frac { \pi } { 4 } = \frac { 3 \pi } { 4 }$
Therefore, the answer is A.

Find the Amplitude, Period and Phase Shift Of y=−2sin⁡(2x−32)y = - 2 \sin \left( 2 x - \frac { 3 } { 2 } \right)y=−2sin(2x−23​)

Find the Amplitude, Period and Phase Shift Of $y = - 2 \sin \left( 2 x - \frac { 3 } { 2 } \right)$