Solving Trigonometric Functions

In this article, we will provide a brief guide to solving trigonometric functions. We will cover the basics of what trigonometric functions are, along with how to solve them using basic algebra. If you’re looking for a more in-depth explanation of how to solve trigonometric functions, we suggest checking out one of our other articles on the subject. Let’s get started!

What Are Trigonometric Functions?

Trigonometric functions are mathematical functions that allow us to model and describe many real-world situations. The most basic trigonometric function is the sine function, which allows us to calculate the ratio of the length of the side of a right triangle opposite to an angle to the length of the hypotenuse. The other two basic trigonometric functions are the cosine and tangent functions, which allow us to calculate the ratios of the other two sides of a right triangle.

These functions can be extended to any angle, not just right angles, by using the unit circle. The unit circle is a circle with a radius of one unit, centred at the origin (0,0) of a coordinate plane. The angle that an arc of the unit circle makes with the positive x-axis is called the radian measure of that angle.

Various Trigonometric Functions

The three most common trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions are used to calculate the ratios of the sides of a right triangle. The sine function (sin) calculates the ratio of the length of the side opposite to an angle to the length of the hypotenuse. The cosine function (cos) calculates the ratio of the length of the side adjacent to an angle to the length of the hypotenuse. The tangent function (tan) calculates the ratio of the length of the side opposite to an angle to the length of the side adjacent to that angle.

How To Solve Trigonometric Functions?

There are three ways to solve trigonometric functions: factoring, graphing, and using trigonometric identities. Let’s take a look at each method.

• Factoring is the process of breaking a number down into smaller parts. You can use factoring to solve trigonometric functions by breaking the function down into smaller parts.
• Graphing is another way to solve trigonometric functions. You can use graphing to find the roots of the function, which are the points where the function intersects the x-axis.
• Using trigonometric identities is a third way to solve trigonometric functions. Trigonometric identities are equations that are true for all values of the variables. You can use trigonometric identities to simplify the function, which will make it easier to solve.

Common Mistakes Made By Students

When solving trigonometric functions, students often make mistakes. Here are some common mistakes made by students:

• Not using the correct formula: There are many different formulas for solving trigonometric functions. Make sure you are using the correct formula for the function you are trying to solve.
• Misusing the Pythagorean Theorem: The Pythagorean Theorem can be used to solve for missing sides in a right triangle. However, many students mistakenly use the theorem to solve for angles.
• Not drawing a picture: When solving trigonometric functions, it is often helpful to draw a picture. This will help you visualize the problem and see what information you are given and what you need to solve.
• Solving for the wrong variable: Make sure you are solving for the variable that is asked for in the problem. Oftentimes, students will solve for a different variable and then use that value to try to solve for the original variable. This will not work and will just give you an incorrect answer.

Conclusion

In this guide, we’ve walked you through the basics of solving trigonometric functions. We started by discussing what trigonometric functions are and how to identify their inverse. Then, we showed you how to use the basic principles of algebra and geometry to solve angles in a triangle. Finally, we wrapped up with a few practice problems so that you can apply what you learned. If you still have questions or need more practice, be sure to check out our other guides on trigonometry or contact your math teacher for help. Good luck!