# Math Help - Solve this trig equation

1. ## Solve this trig equation

sin(3x) = cos(x + pi/4)

Thanks

2. my attempt
sin 3x = cos(x+pi/4)
sin 3x= sin{ pi/2- (x+pi/2)}
sin 3x= sin( pi/4 - x )
gives
3x=pi/4 - x

x=pi/16

3. $\sin(3x) = \cos( x + \frac{\pi}{4} )$

$\sin(3x) = \sin( \frac{\pi}{2} - x - \frac{\pi}{4} )$

$\sin(3x) = \sin( \frac{\pi}{4} - x )$

$3x = 2n\pi + \frac{\pi}{4} - x$

$x = \frac{(8n+1)\pi}{16}$

Or

$3x = (2n+1)\pi - \frac{\pi}{4} + x$

$x = \frac{( 8n + 3 )\pi}{8}$

4. where did 2 n come from?

5. Originally Posted by usagi_killer
where did 2 n come from?
its because there is no restriction to the domain of x .

6. i have plotted this function, sin(3x) - cos(x + pi/4) = 0, for x = 0 to 2pi

it does have 6 roots for x = 0 to 2 pi

using the sum to product formula, we have this

-2 sin (pi/8 -2x) cos (x + pi/8) = 0

this one form does not generate the 6 roots as shown in the plot, i wonder
Attached Thumbnails
{"extraction_info": {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "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, "math_score": 0.9754046201705933, "perplexity": 3820.2413099827663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398445080.12/warc/CC-MAIN-20151124205405-00067-ip-10-71-132-137.ec2.internal.warc.gz"}