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, you can substitute t = 3 into the given function, y = 5 + 3 sin (πt/3 + π/2):
y = 5 + 3 sin (π(3)/3 + π/2) = 5 + 3 sin (π + π/2) = 5 + 3 sin (3π/2)
To evaluate sin (3π/2), you need to recall the unit circle. At this value of the angle, sin (3π/2) = -1. Therefore,
y = 5 + 3(-1) = 5 - 3 = 2
So, when t = 3, the value of the function is 2.
Now, let's determine the period of the function. The period of a trigonometric function is the length of one complete cycle of the function. In this case, the function is of the form y = a + b sin (ct + d), where a, b, c, and d are constants.
The period of a sine function is calculated using the formula: period = (2π)/|c|
In the given function, c is the coefficient of t, which is π/3. Using the formula, we can calculate the period:
period = (2π)/|π/3| = (2π)/(π/3) = 2π * (3/π) = 6
So, the period of the function is 6.
Now, let's go through the options you provided:
0: This is not the value of the function when t = 3.
1/6: This is not the value of the function when t = 3.
π/6: This is not the value of the function when t = 3.
2: This is not the value of the function when t = 3.
3: This is not the value of the function when t = 3.
π: This is not the value of the function when t = 3.
5: This is the correct value of the function when t = 3.
6: This is not the value of the function when t = 3.
Therefore, the correct answer for the value of the function when t = 3 is 5, and the period of the function is 6.