And we can use mnemonic rules such as "the sine of an angle is the opposite side" and "the cosine of an angle is the adjacent side".įor a unit circle that is centered at the origin, the equation that any point \((x, y)\) on it satisfies is:Īny pair \((x, y)\) that belongs to a circle of radius 1 must satisfy the above. Therefore, the operation with trigonometric functions is much easier when the radius of a circle is 1, and then everything becomes much more visual. Where \(\alpha\) is the angle shown in the figure below:īut when \(r = 1\), this is, when the radius is 1 (which is the case in the unit circle), we find that Indeed, it turns out that if we have a point \((x,y)\) in a circle with radius \(r\), then we have that Using the unit circle is super useful to work with trigonometric functions. Trigonometric Functions and the Unit Circle There are other circumstances in which the origin of the angle is not the same as the center of the circle, like in the case of the graph below: If measured in degrees, or \(2\pi/4 = \pi/2\) if measured in radians
#UNIT CIRCLE CHART FULL#
Let us a recall that the measure of an angle is proportional to the amount of the circumference of the circle that the angle spans.įor example, if an angle spans a quarter of the circumference, and its origin is the same as the center of the circle, then the measure of the angle is a quarter of the measure of a full angle, which is 360/4 = 90 The unit circle, or a circle of any radius, is a very practical way of working with angles. Note that we are talking about the two-dimensional case. The name says it clearly: The unit circle is a circle of radius \(r=1\), which for convenience is assumed to be centered at the origin \((0, 0)\). The unit circle crosses Algebra (with equation of the circle), Geometry (with angles, triangles and Pythagorean Theorem) and Trigonometry (sine, cosine, tangent) in one place. The unit circle is one of the most used "laboratories" for understanding many Math concepts.
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