Cosine (cos) equals 0 at specific angles on the unit circle. Specifically, cosine equals 0 when the x-coordinate on the unit circle is 0.
The Unit Circle Explanation
The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the Cartesian plane. For any angle θ, the point where the terminal side of the angle intersects the unit circle has coordinates (cos θ, sin θ). Therefore, the x-coordinate corresponds to the value of cosine, and the y-coordinate corresponds to the value of sine.
Values Where Cosine Equals 0
Cosine equals 0 at the following angles:
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π/2 (90°): At π/2 radians (90 degrees), the point on the unit circle is (0, 1). Therefore, cos(π/2) = 0.
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3π/2 (270°): At 3π/2 radians (270 degrees), the point on the unit circle is (0, -1). Therefore, cos(3π/2) = 0.
General Solution
More generally, cosine equals 0 at θ = π/2 + nπ, where n is any integer. This means:
- ... -5π/2, -3π/2, -π/2, π/2, 3π/2, 5π/2, ...
Summary
In summary, cosine equals 0 at π/2 (90 degrees) and 3π/2 (270 degrees), and at all angles coterminal with these angles. The general solution is θ = π/2 + nπ, where n is any integer.
