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How do you use the graphing calculator to determine whether the equation #costheta(costheta-sectheta)=-sin^2theta# could be an identity?

Answer 1

Pick a value for #theta# like #theta=20^@# and plug it in to both sides to see if it is true. If not then it is not an identity

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Answer 2

Madelyn Adams

To determine whether the equation ( \cos(\theta)(\cos(\theta) - \sec(\theta)) = -\sin^2(\theta) ) could be an identity, follow these steps using a graphing calculator:

Enter the left-hand side of the equation as ( \cos(\theta)(\cos(\theta) - \sec(\theta)) ).
Enter the right-hand side of the equation as ( -\sin^2(\theta) ).
Graph both sides of the equation on the same set of axes.
Observe whether the graphs coincide or overlap for all values of ( \theta ).
If the graphs coincide for all values of ( \theta ), then the equation is likely an identity. If they do not coincide for some values of ( \theta ), the equation is not an identity.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.