Question

1. Fill in the table below to 2 decimal places for the graph of y = sin x and y = 2sin (x-30) for the range
   – 180 ≤ x ≤180 

   xº	-180	-150	-120	-90	-60	-30	0	30	60	90	120	150	180
   Sin xº	0			-1.0	-0.87		0		0.87			0.5
   2 Sin (x – 30)º	1			-1.73	-2.0		-1		1.0			1.73

   Using your graph
2. 1. State the amplitude and the period of the graph y = 2 sin (x-30)0 
   2. Solve the equation
      Sin xº = 2 sin (x-30)º 
   3. Describe fully the transformation that will map y = 2sin (x-30)0 on y = sin x 

Answer 1

1. 
   

   xº	-180	-150	-120	-90	-60	-30	0	30	60	90	120	150	180
   Sin xº	0	-0.5	-0.87	-1.0	-0.87	-0.5	0	0.5	0.87	1.0	0.87	0.5	0.0
   2 Sin (x – 30)º	1	0	-1.0	-1.73	-2.0	0	-1	0	1.0	1.73	2.0	1.73	1.0

      
2. Using your graph
   • State the amplitude and the period of the graph y = 2 sin (x-30)0 
     y = 2sin(x- 30º)
     Amplitude = 3units
     Period = 360º
   • Solve the equation
     Sin xº = 2 sin (x-30)º 
     SinX = 2Sin (x – 30º)
     X = -126º cr 51.50 ±1º
   • Describe fully the transformation that will map y = 2sin (x-30)0 on y = sin x 
     +30
     0 Translation