Trigonometry, Math

Question

Sketch the graph of the equation the on interval . You must find the beginning and the end of a period. Then apply the appropriate reflection, stretching, and vertical shifting:

a) y = 2+2 sin(x+π/2)

b) y = 2-2 cos(x-π/2)

Answer 1

Hi Ham,

The equation

y = 2+2 sin(x+π/2)

can be thought of as y = sin(x) that has been shifted and scaled. For the equation,

y = a * sin(bx+c) + d

a = scale factor - when a is negative, the function will be reflected over the x-axis

b = horizontal stretch - b > 1 = compression, and b < 1 = stretch

c = horizontal shift - negative values shift to the right and positive values shift to the left

d = vertical shift - positive is up, negative is down

The equation

y = 2+2 sin(x+π/2)

is the equation y = sin(x) that has been shifted to the left by π/2, scaled by a factor of 2, and shifted upward by 2 units.

Sin(x) and cos(x) oscillate between [-1,1] for x values [0,2π]

b) y = 2-2 cos(x-π/2)

is the function cos(x) that has been shifted to the right by π/2, reflected over the x-axis, scaled by 2, and shifted upwards two units.

Let me know if this helped!