Solving Trigonometric Equations: Grade 12 Homework Help | Unit Circle Method

In summary, the given equation (2sinx-1)(tanx-1) = 0 can be solved by setting each bracket equal to 0 and finding the roots. The answers for 0<x<2pi are pi/6, 5pi/6, pi/4, and 54/4. The unit circle is used in this process. It is also possible to use the principal solution and the ±180º equations to solve the equation.
  • #1
cybernerd
27
0

Homework Statement



Solve the following equation:

(2sinx-1)(tanx-1) = 0
0<x<2pi

The answers are listed as :

pi/6, 5pi/6, pi/4, 54/4

Homework Equations



I'm told the unit circle is used.

The Attempt at a Solution



I'm attempting to learn this from dijointed class notes for a class I missed...

I iunderstand I need to use each bracket by itself, make rotations around the unit circle and find a certain value and use the x value...problemis, I have no idea how to get started. Could anyone shed some light on this frustrating topic?
 
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  • #2
Hi cybernerd! :smile:
cybernerd said:
Solve the following equation:

(2sinx-1)(tanx-1) = 0
0<x<2pi

I iunderstand I need to use each bracket by itself

Yes, either (2sinx-1) = 0 or (tanx-1) = 0, so roots of either will do. :smile:
… make rotations around the unit circle and find a certain value and use the x value

Sorry, I've no idea what that means in this context …

surely you just find the principal solution, and then use the ordinary ±180º equations? :confused:
 
  • #3


I understand your frustration with trying to solve trigonometric equations using the unit circle method. However, I assure you that with practice and understanding of the unit circle, you will be able to solve these equations effectively.

To solve this specific equation, we can use the Zero Product Property, which states that if two factors multiplied together equal zero, then at least one of the factors must equal zero.

So, we can set each bracket equal to zero and solve for x.

(2sinx-1) = 0
2sinx = 1
sinx = 1/2
x = pi/6 or 5pi/6

(tanx-1) = 0
tanx = 1
x = pi/4

Therefore, the solutions for the equation are x = pi/6, 5pi/6, or pi/4.

To better understand how these solutions were obtained, it may be helpful to draw a unit circle and label the points where sinx = 1/2, tanx = 1, and the corresponding angles. This will give you a visual representation of the solutions and how they relate to the unit circle.

I hope this helps and keep practicing with the unit circle method. It will become easier with time and practice.
 

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the study of triangles and relationships between their sides and angles.

Why is trigonometry important?

Trigonometry is important because it has many practical applications in various fields such as engineering, navigation, astronomy, and physics. It helps in solving real-world problems involving angles and distances.

What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent, which represent the ratios of sides in a right triangle. These functions are used to find missing sides or angles in a triangle.

How is trigonometry used in everyday life?

Trigonometry is used in everyday life in various ways, such as determining the height of a building, calculating the distance between two points, or finding the angle of elevation for a ladder. It is also used in fields like architecture, surveying, and construction.

What is the difference between radians and degrees?

Radians and degrees are units of measurement for angles. One complete circle is equal to 360 degrees or 2π radians. Radians are often used in more advanced trigonometry and calculus, while degrees are commonly used in everyday situations.

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