# Km8,38 Find the value of \theta if it exists

• MHB
• karush
In summary, the value of $\theta$ can be found by setting $\tan(\theta)$ equal to $\sqrt{3}$ and solving for $\theta$. Using the identity $\tan\theta = \frac{\sin\theta}{\cos\theta}$, it can be rewritten as $\frac{\sin\theta}{\cos\theta}=\sqrt{3}$. By observing the unit circle or using a calculator, it can be determined that when $\theta=\frac{\pi}{3}$, the tangent is equal to $\sqrt{3}$.
karush
Gold Member
MHB
Find the value of $\theta$ if it exists
$$\theta=\tan^{-1}\sqrt{3}$$
rewrite
$$\tan(\theta)=\sqrt{3}$$
using $\displaystyle\tan\theta = \frac{\sin\theta}{\cos\theta}$ then if $\displaystyle\theta = \frac{\pi}{3}$
$$\displaystyle\frac{\sin\theta}{\cos\theta} =\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} =\sqrt{3}$$ok I think this is a little awkward since it is observing the unit circle to see what will work
so was wondering if there is a more proper way.

My first thought would be to use a calculator (or, if you are as old as I am, a table of trig functions) but I suspect that is not what you mean. For $tan(\theta)= \sqrt{3}$, imagine an equilateral triangle with all three sides of length 2. Draw a perpendicular from one vertex to the opposite side. That will also bisect the opposites side and bisect the vertex angle. So it divides the equilateral triangle into two right triangles, each with hypotenuse of length 2 and one leg of length 1. By the Pythagorean theorem, The third sides, the altitude of the equilateral triangle, has length $\sqrt{2^2- 1^2}= \sqrt{3}$. So the tangent of the angle opposite that side of length $\sqrt{3}$ is $\frac{\sqrt{3}}{1}= \sqrt{3}$. Of course that angle is one of the original angles of the equilateral triangle so 60 degrees or $\pi/3$ radians.

I'm 74

Just a young guy then! You'd be surprised what geezers most of us are. Nothing else to do, I guess.

we have to let the young (under 70) know our brain didn't implode

just can't remember a D*** thing anymore...

## 1. What is the meaning of "Km8,38"?

"Km8,38" is an expression that represents a distance measurement. The "Km" stands for kilometers and the numbers "8,38" indicate the specific distance in kilometers.

## 2. What does "Find the value of \theta if it exists" mean?

This phrase is asking for the value of an angle, represented by the Greek letter theta (θ), if it exists. This means that there may be a specific angle that satisfies the given conditions, and the task is to find that value.

## 3. How do I solve for \theta in "Km8,38 Find the value of \theta if it exists"?

To solve for θ, you will need to use the given information and apply relevant mathematical concepts and formulas. This may involve using trigonometric functions, algebraic equations, or geometry principles depending on the specific problem.

## 4. Is there a specific formula or method for solving "Km8,38 Find the value of \theta if it exists"?

There is no one specific formula or method for solving this type of problem. It will depend on the given information and the specific conditions of the problem. However, there are general strategies and techniques that can be applied, such as setting up equations, using trigonometric identities, and applying geometric principles.

## 5. What if \theta does not exist in "Km8,38 Find the value of \theta if it exists"?

If θ does not exist, it means that there is no angle that satisfies the given conditions. This could be due to a number of reasons, such as the problem being impossible to solve or the given information being contradictory. In this case, the answer would be that θ does not exist.

Replies
2
Views
1K
Replies
2
Views
1K
Replies
3
Views
1K
Replies
1
Views
887
Replies
2
Views
747
Replies
5
Views
1K
Replies
1
Views
7K
Replies
2
Views
6K
Replies
4
Views
2K
Replies
1
Views
11K