NBCT Mathematics Adolescence And Young Adulthood (AYA) Component 1 Practice Test

Cosine function touches the x-axis at which x-values?

0 and 2pi pi and 2pi 0 and pi pi/2 and 3pi/2

Correct Answer:

pi/2 and 3pi/2

Explanation:

The value where the cosine function crosses the x-axis is where cos x = 0. In one full cycle from 0 to 2π, those x-values are π/2 and 3π/2. At these angles the point on the unit circle lies on the y-axis, so the x-coordinate (which is cos x) is zero. The other numbers don’t give zero because cos 0 = 1, cos π = −1, and cos 2π = 1. Since cosine repeats every 2π, the zeros occur again at π/2 + kπ for any integer k.

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