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Draw the graph of y = 3 sin (x/2 + 11pi/2)

Solution

Using the trigonometry function of sine of the sum of two angles formula: sin (a + b) = sin(a)cos(b) + cos(a)sin(b), so, y = 3 sin (x/2 + 11pi/2) = 3 [sin (x/2) cos (11pi/2) + cos (x/2) sin (11pi/2) ]. Since 11pi/2 = 2 × 2pi + 3pi/2. so, y = 3 [sin (x/2) cos (3pi/2) + cos (x/2) sin (3pi/2) ]. Since cos (3pi/2) = 0 and sin (3pi/2) = -1, so, y = -3 cos (x/2). Its maximum amplitude is 3, minimum amplitude is -3, minimum period T = 2pi ÷ 1/2 = 4pi. Its graph shows on the vodeo.