- #1
Visualizing Sine and Cosine on a Unit Circle: Accurate or Not?
In summary, the conversation discusses the accuracy of displaying sine and cosine on a unit circle and the use of a diagram to illustrate this concept. The diagram is considered to be a better representation than simply describing the relationship between sine and cosine.
- #2
chroot
Staff Emeritus
Science Advisor
Gold Member
- 10,296
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Well, it doesn't really contain much information, and would probably not make sense to anyone who doesn't already know that the cosine is the x coordinate of points along the unit circle and the sine is the y coordinate.
- Warren
- Warren
- #3
Zorodius
- 184
- 0
See the attachment for a diagram that illustrates what I believe you were trying to say.
- #4
Chen
- 977
- 1
Nice, I remember seeing that on the blackboard in my class a few years ago. 
- #5
FlatlineLemon
- 16
- 0
Zorodius said:
i think that's a much better representation.
FAQ: Visualizing Sine and Cosine on a Unit Circle: Accurate or Not?
What are sine and cosine?
Sine and cosine are two mathematical functions used to describe the relationship between the angles and sides of a right triangle. They are commonly used in trigonometry and have applications in fields such as physics, engineering, and mathematics.
How are sine and cosine related?
Sine and cosine are related by the Pythagorean identity, which states that the square of the sine of an angle plus the square of the cosine of the same angle is always equal to 1. This relationship allows us to use one function to find the other.
What is the unit circle and how does it relate to sine and cosine?
The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate system. Sine and cosine are defined as the y and x coordinates, respectively, of a point on the unit circle. This allows us to visualize and understand the behavior of these functions.
How are sine and cosine used in real life?
Sine and cosine have many real-life applications, such as in navigation, music, and engineering. They can be used to model periodic phenomena, such as the motion of a pendulum or the sound waves of a musical instrument. They are also used in calculating distances and angles in navigation systems.
What is the difference between sine and cosine?
The main difference between sine and cosine is their starting points on the unit circle. Sine starts at (0,1) and cosine starts at (1,0). This results in a phase shift of 90 degrees between the two functions. Additionally, sine and cosine have different mathematical properties and can be used for different purposes.