Here's a theorem about the tangent function

In summary, the conversation discusses a theorem about the tangent function and finding a solution to tan x = 1 between 270 and 450 degrees. The proposed method involves finding an expression for all values of x that satisfy the equation and then locating the specific x within the given range. It is also suggested to use the relationship between tangent, sine, and cosine to solve the equation.
  • #1
imdapolak
10
0
1. Here's a theorem about the tangent function. tan(x) = c iff 1: x = tan^-1*c or 2: x = tan^-1*c+n(180) for some integer n. Find a solution to tan x = 1 between 270 and 450 degrees.




2.


3. I am not really sure how to go about starting this problem. I have only two problems in my homework, but no solution to either to self check.
 
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  • #2


The way I would go about solving this is to first find an expression for all values of x that satisfy the equation, and then locate the specific x that falls in that range. They give you the general solution for c in the first sentence. In your case, c = 1.
 
  • #3


In other words, find one angle such that tan x= 1 and if it is not between 270 and 450 degrees add 180 degrees until it is. I suppose you could use a calculator but since tan(x)= sin(x)/cos(x), tan(x)= 1 is the same as sin(x)= cos(x). It should be easy to find one angle x such that sin(x)= cos(x).
 

Related to Here's a theorem about the tangent function

What is the tangent function?

The tangent function is a mathematical function that relates the ratio of the sides of a right triangle to the angle opposite those sides. It is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

What is the theorem about the tangent function?

The theorem about the tangent function is known as the Pythagorean identity. It states that for any angle θ, the square of the tangent of θ is equal to the sum of the squares of the sine and cosine of θ.

What is the significance of the tangent function?

The tangent function is used in many fields, including mathematics, physics, and engineering. It is particularly useful in trigonometry and calculus, as it allows for the determination of angles and slopes of curves.

What is the domain and range of the tangent function?

The domain of the tangent function is all real numbers except for values that result in an undefined tangent, such as π/2 and 3π/2. The range of the tangent function is all real numbers.

What is the relationship between the tangent function and the sine and cosine functions?

The tangent function is related to the sine and cosine functions through the Pythagorean identity. It can also be defined as the ratio of the sine function to the cosine function. Additionally, the graphs of these functions are related, as the tangent function has vertical asymptotes at π/2 and 3π/2, where the cosine function has zeros.

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