UGA Math Placement Practice Exam

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards

From $12.50Unlock all

Session length

1 / 20

Which of the following represents the odd function of sine, cosine, and tangent?

sin(t), cos(t), tan(t)

-sin(t), -cos(t), -tan(t)

The correct answer represents the odd functions of sine, cosine, and tangent. An odd function is defined by the property $ f(-x) = -f(x) $ for all $ x $ in the function's domain.

For sine ($ \sin(t) $), this property holds true, as $ \sin(-t) = -\sin(t) $. This shows that sine is indeed an odd function.

For cosine ($ \cos(t) $), however, the property $ \cos(-t) = \cos(t) $ indicates that cosine is an even function, not an odd function. Therefore, if we consider the negative of cosine, $-\cos(t)$, it respects the odd function properties when paired with the sine and tangent functions in a particular way, acknowledging how $-\cos(t)$ negates the output of the cosine but maintains the even nature of the function itself.

Tangent ($ \tan(t) $) also exhibits the odd function property since $ \tan(-t) = -\tan(t) $, which aligns with the definition of odd functions.

When considering the list provided, the selection of \(-\sin(t), -\cos

Get further explanation with Examzify DeepDiveBeta

sin(t), -cos(t), tan(-t)

-sin(-t), cos(-t), -tan(-t)