In relation to the y-axis the sine wave is in blue and the cosine is in red.
The sine function is called odd because it has rotational symmetry of 180°.
The cosine function is called even because it is reflected about the y-axis.
sin Θ = -sin -Θ; cos Θ = cos -Θ
sin Θ = cos (Θ - π/2) = cos (Θ - 90°)
cos Θ = sin (Θ + π/2) = sin (Θ + 90°)
A negative sign in front of the function inverts it and a number magnifies its y-value.
A number added or subtracted to the function moves it up or down respectively.
A coefficient of theta greater than 1 condenses the waveform and between 1 and zero stretches it out in the x-direction. If the coefficient is negative, it flips it across the y-axis.
A negative constant inside the function shifts the function to the right and a positive constant inside the function shifts it to the left.
In relation to the y-axis the sine wave is in blue and the cosine is in red.
Below is a transformation:
Red is y = sin Θ
Orange is y = sin (Θ + π/4) Notice the red is shifted to the left.
Green is y = sin (2Θ + π/4) Notice the frequency of the orange is doubled and wavelength is halved.
Blue is y = sin (2Θ + π/4) +2 Notice the green is shifted up by 2.
Black is y = ½ sin (2Θ + π/4) + 2 The amplitude of blue is halved.