To determine if a) is on the unit circle, you can do. Sine and cosine functions, algebra and trigonometry by numerade The numeric values of the different trig functions are the lengths of the line segments in the diagram below, if the circle has radius $1$.
Concepts through functions, a unit circle approach to trigonometry offers a comprehensive journey from the foundations of algebra and geometry to the preview of calculus,.
For proving that the unit circle is connected, you could also say that the only subsets of the unit circle which are both open and closed are the full circle and the empty set. Video answers for all textbook questions of chapter 7, the unit circle: There are many ways to make a circle, topologically, and it's not always trivial to see that they are the same. Video answers for all textbook questions of chapter 3, radian measure and the unit circle, trigonometry by numerade
This helped me a lot when trying to visualize what the numeric. It's the circle of radius $1$ with center at the origin. See the stackexchange thread tips for understanding the unit circle, and note the distinction i make in my answer between what students often see as the unit circle and what teachers see as the unit circle. You have the unit circle in $\bbb r^2$, with the inherited topology.
3 if you are studying the unit circle, then b) should be a familiar cartesian coordinate, as it equivalent to the polar coordinate $\left (1,\frac {5\pi} {4}\right)$.
What is it you are trying to memorize about the unit circle?
