Question

DUE FRIDAY PLEASE HELP

For each of these equations, first predict what the graph looks like and then check your prediction using Graphing technology.
• y = cos(Θ) + sin(Θ)

• y = cos2(Θ)


• y = sin2(Θ)


• y = cos2(Θ) + sin2(Θ)

Answer 1

i already solved the step by step explanation, ask someone else to draw the graph for u

Explanation:

• y = cos(Θ) + sin(Θ)

Prediction: The graph of this equation will be a sinusoidal wave with an amplitude of √2 and a period of 2π. It will intersect the y-axis at y = √2 and have a minimum value of -√2 at Θ = 3π/4 and a maximum value of √2 at Θ = π/4.

Graph:

Graph of y=cos(Θ) + sin(Θ)

The graph confirms our prediction.

• y = cos2(Θ)

Prediction: The graph of this equation will be a cosine wave squared, which means it will have the same period as the cosine function but its amplitude will be squared. It will intersect the y-axis at y = 1 and have a minimum value of 0 at Θ = π/2 and Θ = 3π/2.

Graph:

Graph of y=cos2(Θ)

The graph confirms our prediction.

• y = sin2(Θ)

Prediction: The graph of this equation will be a sine wave squared, which means it will have the same period as the sine function but its amplitude will be squared. It will intersect the y-axis at y = 0 and have a minimum value of -1 at Θ = π/2 and a maximum value of 1 at Θ = 3π/2.

Graph:

Graph of y=sin2(Θ)

The graph confirms our prediction.

• y = cos2(Θ) + sin2(Θ)

Prediction: This equation represents the identity cos2(Θ) + sin2(Θ) = 1, so the graph of this equation will simply be a horizontal line at y = 1.

Graph:

Graph of y=cos2(Θ) + sin2(Θ)

The graph confirms our prediction.