Inverse Trig Equation Comparison: Arcsec vs Arctan

Thread starter IniquiTrance
Start date Dec 14, 2009
Tags

Inverse Trig

In summary, an inverse trig equation involves an inverse trigonometric function and is used to find angle measures in a triangle. To solve such an equation, you need to use the corresponding inverse trigonometric function and isolate the angle measure. The most common inverse trig equations involve the inverse sine, cosine, and tangent functions and have restrictions such as limited range and potential lack of solution. In real life, inverse trig equations are used in various fields such as engineering, physics, astronomy, navigation, surveying, and computer graphics.

Dec 14, 2009

IniquiTrance

Homework Statement

I have knocked a problem down to:

[tex]-arcsec \frac{3x}{4}[/tex]

but my textbook gives the answer as:

[tex]arctan \frac{4}{\sqrt{9x^2 - 16}}[/tex]

Are these somehow equivalent?

Thanks

Homework Equations

The Attempt at a Solution

Physics news on Phys.org

Dec 14, 2009

Mark44

Mentor

Insights Author

I don't think so. However, I get arccsc (3x/4) being equal to arctan(4/sqrt(9x^2 - 16))

1. What is an inverse trig equation?

An inverse trig equation is an equation that involves an inverse trigonometric function, such as arcsine, arccosine, or arctangent. These functions are used to find the angle measures of a triangle when given certain side lengths or ratios. The inverse trig equations are used to "undo" the trigonometric functions that were applied to the angle measure.

2. How do I solve an inverse trig equation?

To solve an inverse trig equation, you need to use the inverse trigonometric function that corresponds to the trigonometric function used in the equation. For example, if the equation has a sine function, you would use the arcsine function to solve for the angle measure. Then, you can use algebraic techniques to isolate the angle measure on one side of the equation.

3. What are the common inverse trig equations?

The most common inverse trig equations involve the inverse sine, cosine, and tangent functions. These equations are often used to find the missing angle measure in a right triangle when given the lengths of two sides.

4. Are there any restrictions when solving inverse trig equations?

Yes, there are some restrictions when solving inverse trig equations. For example, the range of the inverse sine and cosine functions is limited to angles between -90 degrees and 90 degrees. This means that the solutions to inverse trig equations must also fall within this range. Additionally, some inverse trig equations may not have a solution if the given information does not meet certain criteria.

5. How are inverse trig equations used in real life?

Inverse trig equations are commonly used in fields such as engineering, physics, and astronomy to solve for unknown angles and distances. They are also used in navigation and surveying to calculate the positions of objects. Inverse trig equations are also used in computer graphics to create realistic 3D images and animations.