What is tan(π/4)?

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Study for the NBCT Mathematics AYA Component 1 exam. Utilize flashcards and multiple-choice questions with detailed explanations for each question. Prepare efficiently for success in your teaching certification journey!

Multiple Choice

What is tan(π/4)?

Explanation:
Tangent represents the ratio of the opposite side to the adjacent side, or equivalently sine divided by cosine, for a given angle. At π/4, the sine and cosine values are both √2/2. So tan(π/4) = sin(π/4) / cos(π/4) = (√2/2) / (√2/2) = 1. This also matches the 45–45–90 triangle picture, where the two legs are equal, giving a ratio of 1. The other options would require a different angle or a zero cosine (undefined), which doesn’t happen at π/4. So the value is 1.

Tangent represents the ratio of the opposite side to the adjacent side, or equivalently sine divided by cosine, for a given angle. At π/4, the sine and cosine values are both √2/2. So tan(π/4) = sin(π/4) / cos(π/4) = (√2/2) / (√2/2) = 1. This also matches the 45–45–90 triangle picture, where the two legs are equal, giving a ratio of 1. The other options would require a different angle or a zero cosine (undefined), which doesn’t happen at π/4. So the value is 1.

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