function y=4-2sin(2t+pi/2), where t is measured in radians. choose one option which gives the value of the function when t=pi radians.
a)0 b)1 c)2 d)4 e)pi/4 e)pi/4 f)pi/2 g)pi h)2pi
y=4-2sin(2t+pi/2) , when t= π
y = 4 - 2sin(2π + π/2) = 4 - 2sin(5π/2)
= 4 - 2sin(π/2) , since π/2 and 5π/2 are coterminal angles.
= 4 - 2
= 2
Cheers Reiny
To find the value of the function when t = pi radians, we need to substitute pi into the expression for y.
Given the function y = 4 - 2sin(2t + pi/2), we can substitute pi for t:
y = 4 - 2sin(2(pi) + pi/2)
= 4 - 2sin(2pi + pi/2)
= 4 - 2sin(3pi/2)
Now, we need to evaluate sin(3pi/2).
In the unit circle, the point corresponding to 3pi/2 (270 degrees) will have a y-coordinate of -1, since it is located at the bottom of the circle.
Therefore, sin(3pi/2) = -1.
Substituting this back into the expression for y:
y = 4 - 2(-1)
= 4 + 2
= 6
So, when t = pi radians, the value of the function y is 6.
Thus, the correct option is not provided. The correct option would be 6.