To rotate a graph, one method involves transforming the variables in the equation that defines the graph. According to the provided reference, you can achieve this rotation by substituting a specific expression into the graph's equation.
Method Described in Reference
The core principle for rotating a graph by a chosen angle $\theta$, as outlined in the reference, is a specific substitution within the graph's equation.
- The Rule: You take the equation of your graph and "change the Y's into X sine theta plus y cos Theta."
- Application: This means wherever the variable 'y' appears in the original equation, you replace it with the expression $(x \sin\theta + y \cos\theta)$.
Example (Illustrative based on rule, not standard math):
If your original graph's equation was $y = x^2$, applying this rule literally would result in the new equation $(x \sin\theta + y \cos\theta) = x^2$. This new equation represents the graph rotated by angle $\theta$, according to this specific method.
The reference states, "That's it that will rotate whatever graph you have by whatever angle Theta you choose."
This substitution method allows you to define the equation of the rotated graph based on the original equation and the desired angle of rotation $\theta$.
