# Finding the Angle Using Arcsec in Trigonometry

• Firestrider
In summary, the conversation is about solving for the angle theta in terms of PI when given the value of secant theta, which is equivalent to [2 * sqrt(3)] / 3. The conversation discusses using the relationship between secant and cosine, and converting the given value to a form that can be used in a unit circle.
Firestrider

## Homework Statement

arcsec([2 * sqrt(3)] / 3)

N/A

## The Attempt at a Solution

I know that this is equivalent to saying sec (theta) = [2 * sqrt(3)] / 3
I don't know how to solve for theta in terms of PI.

I know sec = hyp/adj and the opp side I found was sqrt(3).
When I try to do this in the calculator I get a DOMAIN error, and even if I did get an angle it would not be a whole number, how to I convert this in terms of PI?

If $sec\theta= \frac{2\sqrt{3}}{3}$
That means that cos$\theta$ = ?

Also note that $\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}}$

Yeah, I know cos (theta) = sqrt(3)/3 but I don't know how to find the angle. All the unit circles I see don't give that reference.

No, you do NOT "know cos (theta) = sqrt(3)/3"! What happened to the 2 in "[2 * sqrt(3)] / 3"?

If $sec(\theta)= \frac{2\sqrt{3}}{3}$ then $cos(\theta)= \frac{3}{2\sqrt{3}}$
NOW use what rock.freak667 said.

Last edited by a moderator:

## What is the arcsec problem in trigonometry?

The arcsec problem in trigonometry refers to the difficulty in finding the inverse of the secant function. While most trigonometric functions have well-defined inverses, the secant function does not. This can lead to confusion and errors when solving trigonometric equations.

## Why is the arcsec problem important?

The arcsec problem is important because it affects the accuracy of trigonometric calculations and can lead to incorrect solutions. It also highlights the limitations of trigonometric functions and the importance of understanding their domains and ranges.

## How can the arcsec problem be solved?

The arcsec problem can be solved by using trigonometric identities and properties. One approach is to rewrite the secant function in terms of other trigonometric functions, such as the tangent or cosine. Another approach is to use a calculator or computer program to calculate the inverse of the secant function.

## What are some common mistakes when dealing with the arcsec problem?

Some common mistakes when dealing with the arcsec problem include forgetting to check the domain and range of the function, using the wrong trigonometric identity, or using the wrong inverse function. It is important to double-check calculations and be familiar with the properties of trigonometric functions.

## How can understanding the arcsec problem benefit me as a scientist?

Understanding the arcsec problem can benefit you as a scientist by helping you to accurately and efficiently solve trigonometric equations and problems. It also allows you to better understand the limitations and properties of trigonometric functions, which can be useful in various scientific applications such as physics, engineering, and surveying.

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