For the equation 12 sin 4x 3 n identify i the amplitude i

For the equation = - 1/2 sin (4x + 3 n), identify (i) the amplitude, (ii) the phase shit, and (iii) the period, 2 3 pi pi/2 - 1/2 -4 pi/3 4 1/2 3 pi/4 4 1/2 - 3 pi/4 pi/2 For the equation y = - 1/2 cos (2x - 2pi). Identify (i) the amplitude, (ii) the phase shit, and (iii) the period. 1/2 pi pi 2 2 pi 2 pi 2 pi pi 1/2 pi/2 pi Find the value of the expression. Sin^-1 squareroot 2/2 pi/3 3 pi/4 2 pi/3 cos^-1 squareroot 3/2 pi/4 pi/6 7 pi/4 11 pi/6 tan^-1 squareroot 3/3 5 pi/6 pi/3 pi/6 5pi/4 sec [sin^-1 [- squareroot 3/2]] 1 squareroot 2/2 0 2 cos[sin^-1 1/2] 0 squareroot 3/2 1 squareroot 2/2

Solution

y=-1/2 sin(4x + 3pi)

This is of the form

y=A sin (Bx +C)

where amplitude is A which is always positive

phase shift is -C/B

and period=2pi/B

Therefore for the given question

A=1/2    B=4     and C=3pi

Amplitude=1/2

phase shift= -3pi/4 and period= 2pi/4=pi/2

Hence the correct option is D

11. A=1/2 B=2    C=-2pi

Amplitude=1/2

phase shift= -(-2pi)/2=pi

period=2pi/2=pi

Hence the correct option is A