As the angle θ increases to 90° the value of tan(θ) A. decreases rapidly. B. approaches +1. C. increases rapidly. D. approaches –1.
Mathematics · College · Sun Jan 24 2021
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C. increases rapidly.
As the angle θ in a right-angled triangle increases towards 90°, the value of tan(θ), which is the ratio of the opposite side to the adjacent side, increases rapidly. This occurs because the length of the opposite side gets longer compared to the length of the adjacent side, which remains constant. As θ approaches 90 degrees, the tangent function heads towards infinity, because you are essentially dividing by a very small number (the adjacent side gets closer to zero).