Question

1) How does the amplitude of y = -2sin(x) compare with y = sin x?

a)its is 2 times much

b)it is one half as much

c)it is 2 more

d)it is the same

How does the period of y = sin x compare with y = sin x?

a)its is 2 times much

b)it is one half as much

c)it is 2 more

d)it is the same

Answer 1

standard equation is

y=Amplitude*sin(w*x)+constant

w= 2*$\pi$*f    where w is frequency in radians and f is the frequency in hertz

T= 2$\pi$/w    where T is the time period

Note: For Amplitude always take positive value even if negative value is given .ie. take modulus of Amplitude i.e. never consider negative sign for calculation.

1. ANSWER TO QUESTION ONE

   Amplitude = 2       for y= -2sin(x)

Amplitude= 1         for y = sin(x)

Amplitude of y= -2sin(x) is 2 times much as compare to y= sin(x)

Ans. option a) its is 2 times much

2. ANSWER TO QUESTION TWO

   FORMULA FOR TIME PERIOD (T)

T = 2$\pi\mathbf{}$/w     

Note: always take positive value of w even if it is given with negative"-" sign i.e. never consider negative sign for calculation.

T= 2$\pi$/1 = 2$\pi$   for y = sin(x) = sin(1*x)

T = 2$\pi$/1 = 2$\pi$ for y = -1/2*sin(x) = -1/2*sin(1*x)

Time period of y=sin(x) is same as time period of y= -1/2sin(x)

Ans option d) it is the same