Help with inverse trig functions

In summary, the conversation discusses the problem of finding the value of cot(arcsin(x)) and the correct approach to solve it by imagining a right triangle with one angle theta and using the trigonometric function tan. The expert also points out an error in the given answer, stating that a square is missing.
  • #1
vysero
134
0
Here is my problem:

cot(arcsin(x))

my awnser:

cot= x/(1-x)^1/2

The online program were suppose to use says I am wrong but I am not sure what I did wrong.
 
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  • #2
vysero said:
Here is my problem:

cot(arcsin(x))

my answer:

cot= x/(1-x)^1/2

The online program were suppose to use says I am wrong but I am not sure what I did wrong.
What's the question that you're trying to answer?

The answer you give makes no sense whatsoever.
 
  • #3
Draw a right triangle, with θ being the acute angle in the triangle. Let θ = arcsin(x), and label the sides and hypotenuse according to this definition.

The problem boils down to evaluating cot(θ).

Your answer SHOULD NOT start with "cot =" since cot by itself is meaningless in this context. If you are doing your work on paper, your work should start with cot(arcsin(x)) = ... and end up with what you found, which is actually not too far off.
 
  • #4
The simplest way to do this is to imagine a right triangle with one angle [itex]\theta[/itex], "opposite side" to [itex]\theta[/itex] of length x, and hypotenuse of length 1 so that [itex]sin(\theta)= x/1[/itex] and thus [itex]\arcsin(x)= \theta[/itex].

Now, what is the length of the near side and what is [itex]tan(\theta)= tan(arcsin(x))[/itex]?

You are missing a square in your answer.
 

1. What are inverse trig functions?

Inverse trig functions are mathematical functions that are used to find the angle of a right triangle when given the ratio of its sides. They are the inverse or opposite of the regular trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent).

2. Why do I need to know about inverse trig functions?

Inverse trig functions are useful in various fields such as mathematics, engineering, physics, and navigation. They are used to solve real-world problems involving angles and distances, and are also important in calculus and other advanced mathematical topics.

3. How do I solve problems involving inverse trig functions?

To solve problems involving inverse trig functions, you need to understand the relationship between the sides and angles of a right triangle. You can use the inverse trig functions to find the missing angle or side length by plugging in the known ratios. It is also important to be familiar with the unit circle and trigonometric identities.

4. Do I need a calculator to work with inverse trig functions?

While a calculator can be helpful, it is not always necessary to solve problems involving inverse trig functions. Some basic problems can be solved using mental math or by using trigonometric tables. However, for more complex problems, a calculator may be necessary to obtain accurate results.

5. Are there any common mistakes to avoid when working with inverse trig functions?

Yes, some common mistakes to avoid include mixing up the input and output of inverse trig functions, using the wrong inverse function for a given problem, and forgetting to use the correct unit of measurement (degrees or radians). It is important to carefully read and understand the problem before solving it to avoid these mistakes.

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