solve y=3sin(4pi2+pi/2)+7

To solve the equation y = 3sin(4π/2 + π/2) + 7, let's break it down step by step.

First, simplify the value inside the sine function:
4π/2 + π/2 = 2π + π/2 = 5π/2

Now, substitute this value back into the equation:
y = 3sin(5π/2) + 7

To find the value of sin(5π/2), we need to recall the unit circle. The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the Cartesian coordinate system.

On the unit circle, the angle 5π/2 is equivalent to moving 5/4 of a full revolution clockwise from the positive x-axis. This angle lies in the fourth quadrant of the unit circle.

In the fourth quadrant, the value of the sine function is negative. So, sin(5π/2) is equal to -1.

Now, substitute this value back into the equation:
y = 3(-1) + 7

Next, multiply and simplify:
y = -3 + 7

Finally, calculate the result:
y = 4

Therefore, the solution to the equation y = 3sin(4π/2 + π/2) + 7 is y = 4.