Similarly, if k is -1, the angle is 90° + 180°(-1) = -90°, which is coterminal with 270°. In electrical engineering, it relates to the instantaneous voltage in alternating current circuits.
Cosine Zero Points on the Unit Circle at 90° and 270°
Understanding this scenario requires looking beyond the standard 0 to 360 degree range and considering the cyclical nature of angular measurement. These are 90 degrees (π/2 radians) and 270 degrees (3π/2 radians).
The only locations where this horizontal position is exactly zero are at the top and bottom of the circle. In radians, this is written as θ = π/2 + πk.
Cosine Zero Points on the Unit Circle at 90° and 270°
This inverse relationship between the two primary trigonometric functions is a direct consequence of the Pythagorean identity, where the square of sine plus the square of cosine always equals one. The general solution is best expressed as θ = 90° + 180°k, where k is any integer.
More About When is cosine 0
Looking at When is cosine 0 from another angle can help expand the discussion and give readers a second clear paragraph under the same section.
More perspective on When is cosine 0 can make the topic easier to follow by connecting earlier points with a few simple takeaways.
