Solving Inverse Function: sec(2x+180)=2, 0<x<360

In summary, The conversation is discussing how to solve the equation sec(2x+180)=2, with a given range of 0<x<360. The suggestion is to change it to cos(2x+180)=1/2 and then get rid of the 180, but this would not result in the correct answers for x. Another suggestion is to change the cosine to -cos(2x) = 1/2 or set the argument of the cosine as it stands to the values that have cosine = 1/2 within the specified interval.
  • #1
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I can only find two answers for this equation, whereas the books says it should be four. Can someone enlighten me? Showing the procedure would help:P

(degrees)
sec(2x+180) = 2 0<x<360
 
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  • #2
First write it as cos(2x+180)=1/2.

Then get rid of the 180 (the 180 causes a shift in the graph of cos(2x)).
 
  • #3
Galileo said:
First write it as cos(2x+180)=1/2.

Then get rid of the 180 (the 180 causes a shift in the graph of cos(2x)).

Changing to cosine is a good idea, but you can't get rid of 180 and get the right answers for x. You could change the cosine to -cos(2x) = 1/2, or set the argument of the cosine as it stands to the values that have cosine = 1/2, then solve for x, keeping only the solutions in the specified interval.
 
  • #4
OlderDan said:
You could change the cosine to -cos(2x) = 1/2
That's what I meant by 'getting rid of the 180'.
 
  • #5
Check the range of x:
0 < x < 360
180 < 2x + 180 < 900
 

1. What is an inverse function?

An inverse function is a function that "undoes" the action of another function. In other words, given a function f(x), the inverse function would return the value of x that was originally input into f(x). In mathematical notation, the inverse function is denoted as f^-1(x).

2. How do you solve inverse functions?

To solve inverse functions, you can use the following steps:
1. Rewrite the equation in the form of f(x) = y.
2. Switch the x and y variables.
3. Solve for y.
4. Replace y with f^-1(x) to get the final inverse function.

3. What is the inverse of the secant function?

The inverse of the secant function is the cosine function, cos(x). This means that if you input a value into the cosine function, the output will be the angle whose secant is equal to that value.

4. How do you solve for x in the equation sec(2x+180)=2, 0

To solve for x in this equation, we can follow these steps:
1. Subtract 180 from both sides to get sec(2x) = -178.
2. Take the inverse secant of both sides to get 2x = sec^-1(-178).
3. Divide both sides by 2 to get x = 0.5 * sec^-1(-178).
4. Use a calculator to find the inverse secant of -178, which is approximately -1.577 radians or -90.4 degrees.
5. Since the given range is 0

5. Is there more than one solution for this inverse function?

Yes, there can be multiple solutions for an inverse function. In this case, since the given range is 0

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