the function
y = 5 + 3 sin (pie t /3 + pie /2)
choose one option which gives the value of the funtion when t = 3.
choose the option which gives the period of the function.
from the options below.
0, 1/6, pie/6, 2, 3, pie, 5, 6
wod the value of t=3 be 5 ?
and i don't knw wat the period of the funtion will be. can sum1 help me plz
To find the value of the function when t = 3, we can simply substitute t = 3 into the function.
Substituting t = 3 into the given function:
y = 5 + 3 sin(pi(3)/3 + pi/2)
y = 5 + 3 sin(pi + pi/2)
Now, let's simplify this expression:
Since sin(pi + pi/2) is equal to sin(3pi/2) and the sine function repeats every pi radians, sin(3pi/2) is equal to sin(pi/2). Therefore, we have:
y = 5 + 3 sin(pi/2)
Now, let's evaluate sin(pi/2) using the trigonometric unit circle:
At pi/2 radians, the y-coordinate of the unit circle is equal to 1. Therefore, sin(pi/2) = 1.
Substituting sin(pi/2) = 1 into our expression for y, we get:
y = 5 + 3(1)
y = 5 + 3
y = 8
So, when t = 3, the value of the function is 8.
Now, let's determine the period of the function. The period of a sinusoidal function is the distance between two consecutive peaks or troughs.
The general formula for the period of a function of the form y = a + b sin(c(t - d)) is given by: Period = 2π/|c|
In our given function, y = 5 + 3 sin(pi t/3 + pi/2), the value of c is pi/3. Substituting this into the formula for period, we get:
Period = 2π/|pi/3|
Period = 2π * (3/pi)
Period = 6
Therefore, the period of the function is 6.
In summary, when t = 3, the value of the function is 8, and the period of the function is 6.