Cos(90°)

Definition

The cosine of 90 degrees is equal to 0. This is a fundamental value in trigonometry that arises when examining angles on the unit circle, which is a circle with a radius of 1 centered at the origin. In the context of the unit circle, the cosine function represents the x-coordinate of a point on the circle corresponding to a given angle measured from the positive x-axis.

5 Must Know Facts For Your Next Test

1. The cosine function, cos(θ), represents the horizontal distance from the origin to a point on the unit circle for an angle θ.
2. At 90 degrees, the point on the unit circle is located at (0, 1), meaning there is no horizontal distance, thus cos(90°) equals 0.
3. Cosine values can also be derived using right triangles, where cos(θ) equals the adjacent side divided by the hypotenuse.
4. The cosine function is periodic with a period of 360 degrees, meaning cos(90°) will repeat every full rotation.
5. Understanding cos(90°) is essential for solving problems involving right triangles and circular motion in trigonometry.

Review Questions

• How does cos(90°) relate to the coordinates of points on the unit circle?
  • Cos(90°) relates directly to the coordinates of points on the unit circle as it corresponds to the x-coordinate of the point at that angle. At 90 degrees, this point is (0, 1), indicating that there is no horizontal displacement from the origin. Therefore, cos(90°) equals 0, reflecting that at this angle, all movement is vertical.
• In what ways can understanding cos(90°) help in solving problems involving right triangles and trigonometric identities?
  • Understanding cos(90°) helps in solving problems involving right triangles by recognizing that any angle approaching 90 degrees results in a cosine value of 0. This insight aids in using trigonometric identities and relationships effectively. For example, if one angle in a right triangle approaches 90 degrees, we can easily deduce that its cosine will diminish to zero, simplifying calculations for adjacent and opposite sides.
• Evaluate how cos(90°) contributes to our understanding of periodic functions and their applications in real-world scenarios.
  • Cos(90°) being equal to 0 exemplifies how cosine is a periodic function, repeating every 360 degrees. This periodic nature means that we can predict outcomes in oscillatory systems like sound waves and alternating current in electrical engineering. Knowing specific values like cos(90°) allows us to model these behaviors accurately and make predictions based on angular measurements in practical applications such as navigation and physics.

Related terms

Unit Circle:

A circle of radius 1 centered at the origin of the coordinate plane, used to define trigonometric functions based on angles.

Sine Function: A trigonometric function that gives the y-coordinate of a point on the unit circle corresponding to a given angle.

Angle Measurement: The size of an angle expressed in degrees or radians, which is crucial for defining the values of sine, cosine, and tangent.