# Thread: Trigonometry problem , easy for someone who knows math :)

1. ## Trigonometry problem , easy for someone who knows math :)

2. Is this problem for studying for the test? Or is it a take-home test?

Alpha=x.. k?
cos x=5/13
x is between 270,360 so x is negative of the form (360-x).

cos x= cos -x
therefore, we can take cos x as acute.
but sin x is negative
sin360-x = - sin x

sin(60-x)=sin60*cosX -sin(-X)cos60
=root3 *5/13 + 12/13*1/2
=5root3 + 12
------------
26

cos(45+x)=cos45cosX-sin45sin(-X)
=1/root2*5/13 + 1/root2*12/13
= 17
------
13root2

4. Your addition of angles formula is the right way to go about this. The restriction on x just tells you the sign of sin(x), where you use Pythagorean theorem to find sin(x) without actually needing to solve for x. I would double-check your trig there, especially the sin(60).

5. Hello, TheGame!

$\cos\theta \:=\:\frac{5}{13},\;\;\theta \in Q4$

Find: . $(a)\;\sin(60^o-\theta)$
. . . . . $(b)\;\cos(\theta + 45^o)$

$\cos\theta \:=\:\dfrac{5}{13} \:=\:\dfrac{adj}{hyp}$

$\theta$ is in a right triangle with: $adj = 5,\;hyp = 13$

Pythagorus tells us that: $opp = \pm 12$

Since $\theta$ is in $Q4,\;\sin\theta \:=\:\text{-}\frac{12}{13}$

$(a)\;\sin(60^o - \theta) \;=\;\sin60^o\cos\theta - \cos60^o\sin\theta$

. . . . . . . . . . . . $=\;\left(\dfrac{\sqrt{3}}{2}\right)\left(\dfrac{5} {13}\right) - \left(\dfrac{1}{2}\right)\left(\text{-}\dfrac{12}{13}\right)$

. . . . . . . . . . . . $=\;\dfrac{5\sqrt{3}+12}{26}$

$(b)\;\cos(\theta + 45^o) \;=\;\cos\theta\cos45^o - \sin\theta\sin45^o$

. . . . . . . . . . . . $=\;\left(\dfrac{5}{13}\right)\left(\dfrac{1}{\sqrt {2}}\right) - \left(\text{-}\dfrac{12}{13}\right)\left(\dfrac{1}{\sqrt{2}}\ri ght)$

. . . . . . . . . . . . $=\;\dfrac{17}{13\sqrt{2}}$

6. Also,i use sin^2 x + cos^2 x=1.. another form of pythagoras.. but straight to the point..
{"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": 15, "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/153998-trigonometry-problem-easy-someone-who-knows-math.html", "fetch_time": 1516369168000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2018-05/segments/1516084887981.42/warc/CC-MAIN-20180119125144-20180119145144-00330.warc.gz", "warc_record_offset": 221842331, "warc_record_length": 11406, "token_count": 722, "char_count": 1865, "score": 4.375, "int_score": 4, "crawl": "CC-MAIN-2018-05", "snapshot_type": "longest", "language": "en", "language_score": 0.5283561944961548, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00039-of-00064.parquet"}