Terminal Side

Definition

The terminal side of an angle in the unit circle is the side that extends from the origin to the point where the angle intersects the unit circle. It is a key concept in understanding the sine and cosine functions within the context of the unit circle.

5 Must Know Facts For Your Next Test

1. The terminal side of an angle in the unit circle determines the values of the sine and cosine functions for that angle.
2. The $x$-coordinate of the point where the terminal side intersects the unit circle is the cosine of the angle, and the $y$-coordinate is the sine of the angle.
3. As the angle increases, the terminal side rotates counterclockwise around the unit circle, and the values of sine and cosine change accordingly.
4. The terminal side can be used to visualize and understand the periodic nature of the sine and cosine functions.
5. The orientation of the terminal side (whether it is in the first, second, third, or fourth quadrant of the unit circle) determines the signs of the sine and cosine values.

Review Questions

• Explain how the terminal side of an angle in the unit circle is used to determine the values of the sine and cosine functions for that angle.
  • The terminal side of an angle in the unit circle extends from the origin to the point where the angle intersects the circle. The $x$-coordinate of this point is the cosine of the angle, and the $y$-coordinate is the sine of the angle. As the angle increases, the terminal side rotates counterclockwise around the unit circle, and the values of sine and cosine change accordingly. This relationship between the terminal side and the trigonometric functions is a fundamental concept in understanding the unit circle and its applications.
• Describe how the orientation of the terminal side in the unit circle affects the signs of the sine and cosine values.
  • The orientation of the terminal side, whether it is in the first, second, third, or fourth quadrant of the unit circle, determines the signs of the sine and cosine values. In the first quadrant, both sine and cosine are positive. In the second quadrant, sine is positive, and cosine is negative. In the third quadrant, both sine and cosine are negative. In the fourth quadrant, sine is negative, and cosine is positive. Understanding how the terminal side's position in the unit circle affects the signs of the trigonometric functions is crucial for correctly evaluating and interpreting the values of sine and cosine.
• Analyze how the terminal side can be used to visualize and understand the periodic nature of the sine and cosine functions.
  • The terminal side of an angle in the unit circle can be used to visualize and understand the periodic nature of the sine and cosine functions. As the angle increases, the terminal side rotates counterclockwise around the unit circle, and the values of sine and cosine repeat in a cyclical pattern. This periodic behavior is reflected in the sine and cosine functions, which have a period of $2\pi$ radians or 360 degrees. By observing the movement of the terminal side and its relationship to the trigonometric functions, students can develop a deeper understanding of the underlying principles that govern the periodic nature of sine and cosine.

Related terms

Unit Circle:

A circle with a radius of 1 unit, centered at the origin (0,0) on the coordinate plane, used to define trigonometric functions.

Angle: A geometric figure formed by two rays, or line segments, sharing a common endpoint called the vertex.

Trigonometric Functions: Functions that relate the sides and angles of a right triangle, such as sine, cosine, and tangent.