I can solve for $x$ by taking the arctangent of both sides but I"m not understanding what the equation means. Does the equation represent the interesection between $y = an x$ and $y =1$? Likewise is $sin x = 2$ said khổng lồ be undefined as the two curves vày not intersect for any real $x$ (they don"t cut each other?). I feel that I am missing a key concept in trigonometric equations.

Bạn đang xem: What does $ an x = 1$ mean?

Also lớn find other solutions of $ an x = 1$ bởi vì I just subtract or địa chỉ $pi$ lớn the principle value?

Thanks


*

*

Solving the equation $ an x=1$ means finding every angle $x$ whose tangent is $1$. You can start with $fracpi4$, the principal arctangent of $1$; the tangent has period $pi$, so (as you said) you need to địa chỉ cửa hàng integer multiples of $pi$ to lớn that to lớn get the entire phối of solutions:

$$left\fracpi4+npi:ninBbb Z ight\;.$$

If you’re asked khổng lồ solve $sin x=2$, you can safely say that the phối of solutions is empty ($varnothing$), since $|sin x|le 1$ for all $xinBbb R$.

In neither case is it actually necessary to think in terms of graphs, though it’s certainly possible to bởi vì so: the set of solutions lớn $ an x=1$ is indeed the set of $xinBbb R$ where the graphs of $y= an x$ and $y=1$ intersect, and similarly for $sin x=1$.


*

$ anx$ is the ratio of $sinx$ over $cosx$. Having $ anx=1$ means that $sinx=cosx$.

Now, what angles produce this result?


*

What is your definition of the tangent function? It"s the sine divided by the cosine, which is exactly the same thing as the famous slope formula "rise over run" So if x is the angle a line through the Origin makes with the positive horizontal axis, you are essentially asking for what angle the line has slope 1. Now when you solve the equation, you get 45° và so the line makes 45° with the positive axis.


*

The solutions (also known as roots), if any, of an equation $f(x)=0$ can always be found graphically by plotting $y=f(x)$ and locating the $x$ intercepts.

Your equation $ an x=1$ can be rewritten as $ an x - 1 = 0$. It implies that $f(x)= an x -1$. The plot is as follows & the solutions ($x$ intercepts) are $x$.

*


Thanks for contributing an answer to nofxfans.comematics Stack Exchange!

Please be sure to answer the question. Provide details and share your research!

But avoid …

Asking for help, clarification, or responding to other answers.Making statements based on opinion; back them up with references or personal experience.

Use nofxfans.comJax khổng lồ format equations. nofxfans.comJax reference.

Xem thêm: Vẻ Đẹp Của Xứ Huế Qua 2 Tác Phẩm Đây Thôn Vĩ Dạ Và Ai Đã Đặt Tên Cho Dòng Sông

To learn more, see our tips on writing great answers.


Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy và cookie policy


Not the answer you're looking for? Browse other questions tagged trigonometry or ask your own question.


How to khuyễn mãi giảm giá with identities in which one expression, but not the other, evaluates lớn "undefined" in particular instances
Sketching $y = arctanleft(frace^x-1sqrt3 ight)-arctanleft(frace^x-4sqrt3e^x ight)$
Site kiến thiết / biệu tượng công ty © 2022 Stack Exchange Inc; user contributions licensed under cc by-sa. Rev2022.4.14.41981


Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy.