Does 'using the unit circle' just mean that I use these:
In Quadrant I, theta=beta
In Quadrant II, theta=180-beta
In Quadrant III, theta=180+beta
In Quadrant IV, theta=360-beta
Because the whole lesson we did was about that sort of thing, which is all review from last year, but then at the end we did a quick example saying something about unit circles and every question in my homework is 'using the unit circle'.
The unit circle is the graph of x^2 + y^2 = 1. The radius vector is viewed as the hyp. of a rt triangle and has a magnitude of 1. A vector is assumed to
rotate CCW. So if we start at 0 deg and
calculate the coordinates of the point
where the vector intersects the circle,
we get:
x = 1*cos0 = 1,
y = 1*sin0 = 0,
p(x , y) = (1 , 0).
So coordinates give us the sine and
cosine at any point on the circle.
For a complete graph and more detailed
INFO, GOOGLE,MATH:Unit circle.
Using the unit circle involves more than just using those formulas you mentioned. While those formulas can help you find the values of angles in different quadrants, the unit circle is a geometric representation that allows you to understand the trigonometric functions in a visual way.
The unit circle is a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane. The angles in the unit circle are measured in radians. The key concept behind the unit circle is that the coordinates of any point on the circle can be used to define the values of the sine and cosine functions for that angle.
To use the unit circle, you need to remember a few properties:
1. The angle θ is measured in radians and is the angle formed between the positive x-axis and the line connecting the origin to the point on the unit circle.
2. The coordinates of any point (x, y) on the unit circle represent the values of the cosine (x) and sine (y) of the angle θ.
3. The unit circle contains key angles such as 0°, 30°, 45°, 60°, and 90°, but it also includes angles beyond 90°, up to 360°.
By using the unit circle, you can determine the values of trigonometric functions (sine, cosine, tangent, etc.) for any angle. For example, to find the sine of an angle, locate the point on the unit circle corresponding to that angle, and read the y-coordinate of the point. Similarly, to find the cosine of an angle, you would read the x-coordinate.
When your homework says "using the unit circle," it means you should be using the geometric properties of the unit circle to find the values of trigonometric functions for different angles. This approach helps you understand the underlying concepts visually and provides a solid foundation for solving trigonometric problems.
To answer these types of questions in your homework, visualize the unit circle, identify the angle you are given, locate the corresponding point on the unit circle, and read the required trigonometric value from the coordinates.