Mathematics: Calculate the amplitude, period in radians, the phase shift in radians, the vertical shift, and the maximum and minimum values. Then draw the graphs of sine and cosine in trigonometry.

To calculate the amplitude, period in radians, phase shift in radians, vertical shift, and maximum and minimum values, we need to consider the general form of the sine and cosine functions:

1. Sine function: y = A*sin(B(x - C)) + D
2. Cosine function: y = A*cos(B(x - C)) + D

Where:
- A is the amplitude
- B is the period in radians (B = 2π / period)
- C is the phase shift in radians
- D is the vertical shift

For the sine function:
- Amplitude = A
- Period in radians = 2π / B
- Phase shift in radians = C
- Vertical shift = D
- Maximum value = A + D
- Minimum value = -A + D

For the cosine function:
- Amplitude = A
- Period in radians = 2π / B
- Phase shift in radians = C
- Vertical shift = D
- Maximum value = A + D
- Minimum value = -A + D

Now, let's consider an example:
y = 2*sin(3(x - π/4)) + 1

For the sine function:
- Amplitude = 2
- Period in radians = 2π / 3 ≈ 2.094
- Phase shift in radians = π/4 ≈ 0.785
- Vertical shift = 1
- Maximum value = 2 + 1 = 3
- Minimum value = -2 + 1 = -1

Now, let's draw the graphs of the sine and cosine functions with the given parameters.

Sine Function:

- Amplitude: 1
- Period: 2π radians
- Phase Shift: 0 radians
- Vertical Shift: 0 units
- Maximum Value: 1
- Minimum Value: -1

Graph:

[Image of a sine wave]

Cosine Function:

- Amplitude: 1
- Period: 2π radians
- Phase Shift: π/2 radians
- Vertical Shift: 0 units
- Maximum Value: 1
- Minimum Value: -1

Graph:

[Image of a cosine wave]