# Trigonometry solutions Question

• PhamCy
In summary, the conversation is about finding the solutions of the equation tan(x)=2cos(x)+1 if 0 ≤ x ≤ 2π. The question can be solved by observing the graph or using algorithms and Trigonometry rules. One possible solution is to substitute tan(x) with sin(x)/cos(x) and solve for cos(x). Another approach is to turn the equation into a polynomial and find the roots using methods like Newton's method.
PhamCy

Here's the question.
Find the solutions of the equation tan(x)=2cos(x)+1 if 0 ≤ x ≤ 2π.
I know this question can be solved by observing the graph but is there any other ways (like algorithms OR some Trigonometry rules) to solve this, I couldn't figure that out.
Thank you for those who noticed my question.

[Moderator's note: Moved from a technical forum and thus no template.]

Last edited by a moderator:
Hello PhamCy, !

For example: substitute ##\tan x = {\sin x\over \cos x}## and see where it leads you

Greg Bernhardt
BvU said:
Way beyond what you can solve analytically with high school mathematics. WolframAlpha knows how to solve it analytically, here is one of the solutions:

Oops, I 'missed' the +1 which makes things difficult

Delta2 and Klystron
You could express the relationship as a polynomial in ##\cos\theta##, and then find the roots of the polynomial using something like Newton's method.

Delta2
Turn everything into $\cos x$ to get:
$$4\cos^{4}x+4\cos^{3}x+2\cos^{2}x-1=0$$
From here solve it using whatever method you like. I would advise you plotting the polynomial first.

Delta2

## 1. What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships and properties of triangles and the calculations involving angles and sides of triangles.

## 2. Why is Trigonometry important?

Trigonometry is used in a variety of fields such as engineering, physics, and navigation. It helps us understand and solve problems involving angles and distances, making it a crucial tool in many real-world applications.

## 3. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. Other trigonometric functions include cosecant, secant, and cotangent, which are reciprocals of the basic functions.

## 4. How do I solve trigonometric equations?

To solve a trigonometric equation, you can use the unit circle, trigonometric identities, or trigonometric equations. It is important to understand the properties and relationships of trigonometric functions and use appropriate techniques to simplify the equation and find the solution.

## 5. What is the difference between radians and degrees in Trigonometry?

Radians and degrees are two units for measuring angles. Radians are based on the radius of a circle, while degrees are based on dividing a circle into 360 equal parts. In Trigonometry, radians are often used because they provide a more natural measure for trigonometric functions.

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