Trigonometric Function Homework: Solving sin^2 (x - pi/4) = 1

In summary, the conversation discusses finding solutions for the formula sin^2(x - pi/4) = 1. One approach is to take the square root of both sides, resulting in two equations involving sin(x-pi/4). By finding solutions for each equation and combining them, the solutions for the original formula can be determined.
  • #1
nvez
21
0

Homework Statement


Pardon me first of all for any mistakes, I study in a French school so I might use incorrect terms

I have to find the solutions for the following formula:

sin^2 ( x - pi/4 ) = 1


Homework Equations


None?


The Attempt at a Solution


I've mostly only worked with regular sins, not those that are to the power of n..

most of the time i'd isolate everything then do arcsin(...) and so on but I am not sure what to do exactly here.
 
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  • #2
You have something being squared to produce 1. That means the thing being squared is either 1 or -1. This gives you two equations involving sin(x - pi/4). Find solutions for each one.
 
  • #3
if you take the square root of both sides, on the left side you will get sin(x- pi/4)

and +/- 1 on the right side. Take each case and find x, then combine all of the answers.
 

What is a trigonometric function?

A trigonometric function is a mathematical function that relates the sides and angles of a right triangle. It is used to solve problems involving triangles, such as finding missing sides or angles.

What are the 6 main trigonometric functions?

The 6 main trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent. These functions are used to calculate the ratios of the sides of a right triangle.

How are trigonometric functions used in real life?

Trigonometric functions are used in a wide variety of real-life applications, such as engineering, architecture, navigation, and physics. They are also used in fields like music theory and graphics design.

What is the unit circle and how is it related to trigonometric functions?

The unit circle is a circle with a radius of 1, centered at the origin of the coordinate plane. It is used to understand the properties of trigonometric functions and their relationships with each other.

What is the difference between sine and cosine?

Sine and cosine are both trigonometric functions, but they have different definitions and properties. Sine is the ratio of the opposite side to the hypotenuse in a right triangle, while cosine is the ratio of the adjacent side to the hypotenuse.

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