Working with a sinusoidal function
This question concerns the function
y/3 = 3+ 4sin [3x+ pi ]
Where x is measured in radians.
(1) Choose the one option which gives the value of the function when x= pi/2
(2) Choose the one option which gives the period of the function.
Options for questions 1 and 2.
A 1
B. 2
C. 3
D. 4
E. pi/3
F. 2pi/3
G. pi
H. 3pi
https://brainmass.com/math/trigonometry/working-sinusoidal-function-7121
SOLUTION This solution is FREE courtesy of BrainMass!
(1)
our function is
y/3 = 3+ 4sin [3x+ pi ]
when x=pi/2
We have, 3x + pi = (3pi/2)+pi = 5pi/2 = (2pi + pi/2)
Sin function repeats itself when we add 2pi to it
Hence Sin(2pi + pi/2)= Sin(pi/2) = 1
Substitute this value back to the given function and find the value of y.
y/3 = 3+ 4sin [3x+ pi ] Gives the answer y = 21
Case1
y = {3+4(sin[3x+ pi])/3} Gives the answer y = 5
Because Sin(5pi/6)= 0.5 )
Case2
y = 3+4 Sin[3x+(pi/3)] Gives the answer y = 1 (One among your ans)
Sin (3x+pi/3)= Sin(3pi/2 + pi/3) = Sin(11pi/6) = -0.5
y = 3+ (4 x -0.5 ) = 3-2= 1
(2)
A periodic function can be defined as any function for which,
f(x) = f (x + T) ......(i) for all x.
(that is, value of the function is the same after we add another constant (T) to it)
The smallest constant T which satisfies the above equation is called the period (or the fundamental period) of the function.
The period of the function y = sin Ax is 2pi/A.
Note that A = | A |
The function's value must remain invariant as we use x in it. The smallest value of x for which the function is invariant is the period.
This gives, x = 2(pi/3) (Answer is F)
We need not consider other values as the only variable is x.
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