Introduction

Trigonometry is one of the most important topics in mathematics. Learning how to find the exact values of trigonometric functions can help you understand other topics, such as calculus, more easily. In this article, we will discuss the best ways to find the exact values of trigonometric functions in 2023.

What is a Trigonometric Function?

A trigonometric function is a function of an angle. Trigonometric functions are used to define the relationships between the angles and sides of triangles. The six most commonly used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec) and cosecant (csc). These functions are usually abbreviated as just their initial letters.

Using a Calculator to Find Exact Values

The easiest way to find the exact values of trigonometric functions is by using a calculator. Most calculators have a special button that allows you to enter in the angle and then calculate the exact values of the trigonometric functions for that angle. For example, if you enter in 30 degrees, the calculator will give you the exact values of sin(30), cos(30), tan(30), cot(30), sec(30) and csc(30).

Using the Unit Circle to Find Exact Values

The unit circle is a circle with a radius of 1. It is used to help visualize the relationships between the angles and sides of a triangle. By using the unit circle, you can calculate the exact values of the trigonometric functions for any angle. To do this, start by drawing a circle with a radius of 1. Then, draw a line from the center of the circle to any point on the circle. The angle formed by the line and the radius is the angle that you are trying to calculate the exact values for.

Using the Triangle Method to Find Exact Values

The triangle method is another way to find the exact values of trigonometric functions. To do this, start by drawing a triangle. Then, label the angles with the angle that you are trying to calculate the exact values for. Next, draw a line from the origin of the triangle to the angle that you are trying to calculate. Finally, calculate the lengths of the sides of the triangle using the Pythagorean Theorem. Once you have the lengths of the sides, you can calculate the exact values of the trigonometric functions for the angle.

Using the Triangle Method With the Unit Circle

The triangle method can also be used in combination with the unit circle to find the exact values of trigonometric functions. To do this, start by drawing a circle with a radius of 1. Then, draw a line from the origin of the unit circle to any point on the circle. Next, draw a triangle with the same angle as the one formed by the line and the radius of the circle. Finally, calculate the lengths of the sides of the triangle using the Pythagorean Theorem. Once you have the lengths of the sides, you can calculate the exact values of the trigonometric functions for the angle.

Conclusion

Finding the exact values of trigonometric functions can be a challenging task, but there are several methods that can be used to simplify the process. By using a calculator, the unit circle, or the triangle method, you can easily find the exact values of trigonometric functions in 2023. With a bit of practice, you will be able to find the exact values quickly and accurately.