Flashcard 15 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

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The correct answer is:

\[\sin\;\theta = \frac{opposite}{hypotenuse}\] \[\cos\;\theta = \frac{adjacent}{hypotenuse}\] \[\tan\;\theta = \frac{opposite}{adjacent}\] \[\csc\;\theta = \frac{1}{\sin\;\theta} = \frac{hypotenuse}{opposite}\] \[\sec\;\theta = \frac{1}{\cos\;\theta} = \frac{hypotenuse}{adjacent}\] \[\cot\;\theta = \frac{1}{\tan\;\theta} = \frac{adjacent}{opposite}\]

Explanation:

The trigonometric functions relate the side lengths of a right triangle to each other. The mnemonic SOH CAH TOA is useful for remembering the definitions of sine, cosine, and tangent. To remember that cosecant is \(\frac{1}{\sin\;\theta}\) and that secant is \(\frac{1}{\cos\;\theta}\), note that there is only one co- prefix per relation.

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