## Trigonometry (11th Edition) Clone

$cos~(tan^{-1}~(\frac{4}{5})) = \frac{5\sqrt{41}}{41}$
$\theta = tan^{-1}(\frac{4}{5})$ $tan~\theta = \frac{4}{5} = \frac{opposite}{adjacent}$ Note that $\theta$ is in quadrant I. We can find the value of the hypotenuse: $hypotenuse = \sqrt{4^2+5^2} = \sqrt{41}$ We can find the value of $cos~\theta$: $cos~\theta = \frac{adjacent}{hypotenuse}$ $cos~\theta = \frac{5}{\sqrt{41}}$ $cos~\theta = \frac{5}{\sqrt{41}}~\frac{\sqrt{41}}{\sqrt{41}}$ $cos~\theta = \frac{5\sqrt{41}}{41}$ Therefore, $cos~(tan^{-1}~(\frac{4}{5})) = \frac{5\sqrt{41}}{41}$
{"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": "https://www.gradesaver.com/textbooks/math/trigonometry/CLONE-68cac39a-c5ec-4c26-8565-a44738e90952/chapter-6-quiz-sections-6-1-6-3-page-282/4a", "fetch_time": 1696141842000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2023-40/segments/1695233510781.66/warc/CC-MAIN-20231001041719-20231001071719-00375.warc.gz", "warc_record_offset": 857639563, "warc_record_length": 11988, "token_count": 247, "char_count": 583, "score": 4.09375, "int_score": 4, "crawl": "CC-MAIN-2023-40", "snapshot_type": "latest", "language": "en", "language_score": 0.5154796838760376, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00008-of-00064.parquet"}