π/6

Definition

The angle π/6, also known as 30 degrees, is a fundamental angle in trigonometry and is closely related to the inverse trigonometric functions. This angle is particularly important in the study of 6.3 Inverse Trigonometric Functions, as it serves as a reference point for understanding the behavior and properties of these functions.

5 Must Know Facts For Your Next Test

1. The angle π/6 is equal to 30 degrees, and it is one of the special angles commonly used in trigonometry.
2. In the unit circle, the coordinates of the point representing π/6 are ($\frac{\sqrt{3}}{2}$, $\frac{1}{2}$).
3. The trigonometric ratios for the angle π/6 are: $\sin(\pi/6) = \frac{1}{2}$, $\cos(\pi/6) = \frac{\sqrt{3}}{2}$, and $\tan(\pi/6) = \frac{1}{\sqrt{3}}$.
4. The inverse trigonometric functions, such as $\sin^{-1}$, $\cos^{-1}$, and $\tan^{-1}$, can be used to find the angle given the value of the trigonometric ratio, and the angle π/6 is a common reference point for these functions.
5. Understanding the properties and behavior of the angle π/6 is crucial for solving problems involving inverse trigonometric functions, as it serves as a foundation for more complex trigonometric relationships.

Review Questions

• Explain the significance of the angle π/6 in the context of inverse trigonometric functions.
  • The angle π/6, or 30 degrees, is a fundamental angle in trigonometry and is particularly important in the study of inverse trigonometric functions. This angle serves as a reference point for understanding the behavior and properties of these functions, as the trigonometric ratios for π/6 are commonly used in the evaluation and application of inverse trigonometric functions. Specifically, the values of $\sin(\pi/6)$, $\cos(\pi/6)$, and $\tan(\pi/6)$ are used to determine the corresponding inverse trigonometric function values, which are essential for solving problems involving inverse trigonometric functions.
• Describe the relationship between the angle π/6 and the unit circle.
  • The angle π/6 is closely tied to the unit circle, which is a fundamental tool in the study of trigonometric functions. In the unit circle, the coordinates of the point representing the angle π/6 are ($\frac{\sqrt{3}}{2}$, $\frac{1}{2}$). These coordinates are derived from the trigonometric ratios for the angle π/6, which are $\sin(\pi/6) = \frac{1}{2}$, $\cos(\pi/6) = \frac{\sqrt{3}}{2}$, and $\tan(\pi/6) = \frac{1}{\sqrt{3}}$. Understanding the relationship between the angle π/6 and its representation in the unit circle is crucial for visualizing and interpreting the behavior of inverse trigonometric functions.
• Analyze how the properties of the angle π/6 can be used to solve problems involving inverse trigonometric functions.
  • The properties and characteristics of the angle π/6 can be leveraged to solve a variety of problems involving inverse trigonometric functions. For example, knowing the trigonometric ratios for π/6 allows you to easily determine the corresponding inverse trigonometric function values, such as $\sin^{-1}(\frac{1}{2}) = \pi/6$ or $\cos^{-1}(\frac{\sqrt{3}}{2}) = \pi/6$. Additionally, the angle π/6 can be used as a reference point to understand the behavior and properties of inverse trigonometric functions, such as their periodicity, domain, and range. By leveraging the well-known characteristics of π/6, you can develop a deeper understanding of inverse trigonometric functions and apply this knowledge to solve more complex problems in the context of 6.3 Inverse Trigonometric Functions.

Related terms

Radian: A unit of angular measurement in which the measure of an angle is the ratio of the length of the arc subtended by the angle to the radius of the circle.

Unit Circle: A circle with a radius of 1 unit, used to define and study trigonometric functions.

Trigonometric Ratios: The ratios of the sides of a right triangle, such as sine, cosine, and tangent, which are used to define and study trigonometric functions.