Trigonometric equations are used when dealing with problems in solid geometry, planimetry, astronomy, physics, and other spheres. Equation assignments can be challenging for students. How to do my trigonometry homework with equations easily? In this case, you will be helped by special services. Experts who work there will be able to solve problems with equations of any complexity.
The aim of this article is to help you solve Trigonometry Homework equations, explore their application to solving equations of increased complexity and problems of various contents.
What are Trigonometry Homework equations?
An equation containing an unknown quantity under the trigonometric function sign is called a trigonometric equation. Some of the trigonometric equations are directly solved by reducing them to their simplest form, sometimes with a preliminary decomposition of the left side of the equation into factors when the right side is equal to zero. In some cases, it is possible to replace the unknowns in such a way that the trigonometric equation is transformed into an algebraic equation that is “convenient” for solving.
How to solve trigonometric equations?
Usually, students solve such equations in two ways. The first one is using a trigonometric circle and your logic. We will explore this path here. The second one is using formulas and memory.
The first way is reliable, clear, and hard to forget. This method is perfect for not only dealing with trigonometric equations but also for working with inequalities and all kinds of non-standard examples. You should remember that logic is much stronger than your memory!
Use a trigonometric circle
Here you need elementary logic and a trigonometric circle. A trigonometric circle can be used in whatever equation you solve. Everything is the same with solving problems related to sines, cosines, tangents, and cotangents topics. The solution principle is the same.
Let’s consider any elementary trigonometric equation. For example:
cosx = 0.5.
Y need to find X. Speaking in layman’s terms, you should find the angle (x), the cosine of which is 0.5. Draw a cosine, which is equal to 0.5 on your circle, and you will see the angle. After that, you just need to write down the answer.
Other methods for dealing with trigonometric equations
While working with trigonometric equations, all problems are reduced to bringing to such a form that the elementary trigonometric function is on the left, and the number is on the right. After this is achieved, the value of the function argument should be found using one of the basic formulas for expressing the argument in terms of inverse trigonometric functions.
- Algebraic equations with respect to the trigonometric function. It is necessary to replace the unknowns in such a way that the trigonometric equation is transformed into an algebraic equation that is “convenient” for solving.
- Reducing the order of an equation. Doubling formulas allow the squares of the sine, cosine, and their products to be replaced by linear functions of the sine and cosine of the double angle. It is advantageous to make such substitutions since they lower the order of the equation.
- Use of trigonometric addition formulas and their consequences. Sometimes in equations, there are trigonometric functions of multiple angles. In such cases, you need to use addition formulas.
- Homogeneous equations. An equation in which each term has the same degree is called homogeneous. It can be solved by dividing by the highest power of the sine (or cosine).
The study of trigonometric equations allows students to master the specific mathematical knowledge necessary for application in practical activities, for the study of related disciplines, the development of mental abilities, the ability to extract educational information based on a comparative analysis of graphs, and independently perform various creative work. But if students have difficulty solving such equations, it is better to ask for help on https://prohomeworkhelper.com/. An expert will help you with any trigonometric function.