# Thread: x=pi/2 is a solution?

1. ## x=pi/2 is a solution?

Solve $\displaystyle 2/(\cot {x}) + 3/(\csc {x}) = 0$, $\displaystyle 0<x<2\pi$.

After a few steps, I obtained

$\displaystyle (\sin {x})(2+3 \cos [x}) = 0$

$\displaystyle \sin {x} = 0$ or $\displaystyle \cos {x} = -2/3$

From $\displaystyle \sin {x} = 0$, I obtained the solution $\displaystyle x=\pi/2$. Is $\displaystyle x=\pi/2$ is a solution?

2. ## Re: x=pi/2 is a solution?

Originally Posted by woo
Solve $\displaystyle 2/(\cot {x}) + 3/(\csc {x}) = 0$, $\displaystyle 0<x<2\pi$.

After a few steps, I obtained

$\displaystyle (\sin {x})(2+3 \cos [x}) = 0$

$\displaystyle \sin {x} = 0$ or $\displaystyle \cos {x} = -2/3$

From $\displaystyle \sin {x} = 0$, I obtained the solution $\displaystyle x=\pi/2$. Is $\displaystyle x=\pi/2$ is a solution?
Hints:
1. Look at the first term in the original equation.
2. What is csc(0)?
3. Is x = 0 permitted in the original equation?

-Dan

3. ## Re: x=pi/2 is a solution?

Originally Posted by woo
Solve $\displaystyle 2/(\cot {x}) + 3/(\csc {x}) = 0$, $\displaystyle 0<x<2\pi$.
After a few steps, I obtained $\displaystyle (\sin {x})(2+3 \cos [x}) = 0$
$\displaystyle \sin {x} = 0$ or $\displaystyle \cos {x} = -2/3$
From $\displaystyle \sin {x} = 0$, I obtained the solution $\displaystyle x=\pi/2$. Is $\displaystyle x=\pi/2$ is a solution?
Did you even bother to look at the graph?

4. ## Re: x=pi/2 is a solution?

$\sin{x} = 0 \implies x = k\pi$, which are not valid solutions.

the Wolfram graph does not show the point discontinuities on the x-axis at integer multiples of $\pi$

The valid solutions are where $x = \arccos\left(-\dfrac{2}{3}\right)$

5. ## Re: x=pi/2 is a solution?

Thanks a lot.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://mathhelpforum.com/trigonometry/275852-x-pi-2-solution.html", "fetch_time": 1529756908000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2018-26/segments/1529267864958.91/warc/CC-MAIN-20180623113131-20180623133131-00451.warc.gz", "warc_record_offset": 204899631, "warc_record_length": 11078, "token_count": 616, "char_count": 1719, "score": 4.28125, "int_score": 4, "crawl": "CC-MAIN-2018-26", "snapshot_type": "latest", "language": "en", "language_score": 0.7517957091331482, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00023-of-00064.parquet"}