3. $y = - 2sin(x)$\nphase shift: ______ period: ______\nvertical shift: ______ amplitude: ______

Explanation:

Step1: Recall the general form of a sine function

The general form of a sine function is (y = A\sin(B(x - C))+D).

Step2: Identify the values for each parameter in (y=-2\sin(x))

• For phase shift: In the formula (y = A\sin(B(x - C))+D), the phase shift is (C). In (y=-2\sin(x)), (C = 0).
• For period: The formula for the period of (y = A\sin(Bx)) is (T=\frac{2\pi}{|B|}). Here (B = 1), so (T=\frac{2\pi}{1}=2\pi).
• For vertical shift: In the formula (y = A\sin(Bx)+D), the vertical shift is (D). In (y=-2\sin(x)), (D = 0).
• For amplitude: The formula for the amplitude of (y = A\sin(Bx)) is (|A|). Here (A=-2), so (|A| = 2).

Answer:

Phase shift: (0) Period: (2\pi) Vertical shift: (0) Amplitude: (2)