From 716bb343b1cc0d916e60c6a36c23aadd10218447 Mon Sep 17 00:00:00 2001 From: zleyyij <75810274+zleyyij@users.noreply.github.com> Date: Mon, 23 Sep 2024 11:51:45 -0600 Subject: [PATCH] vault backup: 2024-09-23 11:51:45 --- education/math/MATH1060 (trig)/Graphing.md | 10 ++++++++++ education/math/MATH1060 (trig)/Identities.md | 4 +++- .../math/MATH1060 (trig)/assets/graphsincos.png | Bin 0 -> 15576 bytes 3 files changed, 13 insertions(+), 1 deletion(-) create mode 100644 education/math/MATH1060 (trig)/Graphing.md create mode 100644 education/math/MATH1060 (trig)/assets/graphsincos.png diff --git a/education/math/MATH1060 (trig)/Graphing.md b/education/math/MATH1060 (trig)/Graphing.md new file mode 100644 index 0000000..b1a9603 --- /dev/null +++ b/education/math/MATH1060 (trig)/Graphing.md @@ -0,0 +1,10 @@ +![A graph of sine and cosine](./assets/graphsincos.png) + +Given the above graph: +- At the origin, $sin(x) = 0$ and $cos(x) = 1$ +- A full wavelength takes $2\pi$ + +# Manipulation +| Formula | Movement | +| ------------------ | -------- | +| $ y = cos(x) - 1 $ | | diff --git a/education/math/MATH1060 (trig)/Identities.md b/education/math/MATH1060 (trig)/Identities.md index 3ed3245..f45f19a 100644 --- a/education/math/MATH1060 (trig)/Identities.md +++ b/education/math/MATH1060 (trig)/Identities.md @@ -65,4 +65,6 @@ Applying the exponent gives us $\frac{49}{625}$, so we can do this: $$ \frac{625}{625} - \frac{49}{625} = \frac{576}{625} = sin^2\theta $$ Getting rid of the exponent: -$$ \sqrt{\frac{576}{625}} = $$ +$$ \sqrt{\frac{576}{625}} = \frac{24}{25} = sin\theta $$ + +From there, you can find the rest of the identities fairly easily. \ No newline at end of file diff --git a/education/math/MATH1060 (trig)/assets/graphsincos.png b/education/math/MATH1060 (trig)/assets/graphsincos.png new file mode 100644 index 0000000000000000000000000000000000000000..8adaf60fed0c55f0ac225afd21cd861b463dc71b GIT binary patch literal 15576 zcmbWe1z1(>);7980ci=5kd$ta?nb)1ySrQIP6?$%1WD-zk(BQ4ZV;sVJj=cJxA)oK zf6jHTGriu)yXKm6t|vy^V~l%5D9THsBH<%JAP`ikw_?f=2uwTpkNz1fxU$Sfz5@O{ zwGfsQhCnLfknfD(z-JPZx5{!5h&Lq!@-7$xxdE5n?LZ)I%n-<)Aq2vc27$bE%xF~N z17E-!%Sehr9-;p}w|q+iR}fsKj%@!Di0>n;lsk(k4XkCwETS0M=LR}%o=G_%5B}>-r%pl07VG@&_rYO`$M(BQdfA55nN=?>tlx22#|IlV}dEmJ8(aSw6^Wz(f*x>M=%qShrG|Jy$ zLyd52mHziB)b4{3?th<*2+VLp|NBJyF(yARuW-^DCjz``)ESGIc)7*r())am20QX_ zzOG6hrK3D1CGPi+Tl?i7epXgiFfcIdzv2{RWK0TiLs{g>CF<>}Byt=P2 zb|xk+yJLAc4BF+|f1f2tmY)1993&Y>q@}I>JThnlo;p7QSY_P73H(*@g^a#C_~ zF{*FcHP*?Rd0Z}A17K-7BN>g`#8DP&Y^E0$bW_qr2_U&Yl!*xl(m#FT@jkO8VrND% zsm3jX&KXS3VYNMk9C~m6w+XJU)OQ zNa)|hjObii($5_&S4HW-rE-2fkQ5Tq)tf}6MG$IK&)EmIg#&sjk6}gW*gVJQ8bG{$)T0H$p&!%&sDlK2#?9!3|FRu>Q(fWE)eEdkhTzaH{+|7#cXe7TM&!q%j z=qM@}d~|el2A`Mn{#5C32DeJe;Fq=abv<3(qvckE(agMuE75A>>Ed5t&7G?fH0$?1+cC1S;WhmEu0NG&xzVkEX~}=&voHeM ztDfOuLDwC{@q9TZy~Yn&S^npHlR&27;Nc}CB`MS-jexchrqE@6@sMl0W ztxnOnkRO(mG;XtBwUfTJyKA*VwSad%_}RI^_xjH!BO~MJ=;)oCF>W^(%Z1Ngo^s*0 zZ{MP#kY&1_^R=|${gLq{_MF7##(gNB>7Au7pY7{*oQKNl$vi{3qsoCr1 zY?px3{uzQ~>?=G>%rB#sKr6YZSuw5Bi6Os>OmAZ6H0Hf4q}@>tI8@p8UA`)9-#bcMh~# zCY2E=Y~S#3wqU@6;KNB=7QYW{ctpfU4!gOB``gQd+0)f9V(>v#b2LwtmP$75vns8} z;oJ*s>@)MsI2c?K^};6@GuX{aL>R`w9jba4~BECh|hS+1=fKhEtApo{=EqfOxZUB;P*6Td=K-x05D);n2V89w z4g;9Y!&(&6#qZ^S-%BldGO4i75D~ducSeAf?T#fRz{X}XA4t1g4rtXV(+8uP15TR2 zle(itDU=1ndZGXW10&(nr@f60a@(J_78Z3rm-ed(q{RMLIq?TTr{Un>8X6jYw?6vI z%g3tHzOeUc@%T-&9NY(WGWtL4euwZ=Y&bXQGS*d8z>wU%Sn;Pu-vgpN1I#BzGH@Gj zPzIs4apupNg&-!~o|gpYfBrbTx=!>KPAF2nzW&~&hsrjow20;o&(J&m zO?ee@Ju9m~J*L&=Mk1bfkm2zChA_i~al@dn{it?b!n~zcIM7p6RKLk@A2~h-u-&}Q z^Xp?Tw&709xQV>+a71{gk)tu+T>GRFp?c7UZc-sYH!;=1<*xp)!bCllsb5)z@PX%h zp*DM~+y24jQvdF3Qb{SQiVO`6jWMEW&j?NBhoD-7fU0Y`_<64nr;l3q#Qk=Z&MzGn z&$0G>GB1m;3?xMoF&{MwRd24ZcUd`2JE30tXraO3I4*8y)Dz!97>DHD%G=n(!uyqh zHoZa{zal2m2*+j&_Bk1!ny-^)`BjxW#brISA0e$|N!T)e)Y`N)Gjx%iQ1Ij^a)_k^ic@o?^GdZe-=jYMiMeoZ%2Po6t zblEacFW^a=IZh}VH$)got`ZD5%u+Sh$6e==b%k*yI*eL@ zd-%@iYwPh)i1ln@ViFi`NM(=Smzc_heA>Dn+I5I$68&$Viq9kvK0~%_Be3yJx1au^ zP2wv?j9A5BMqov*(h>SpaX2eaSBSb)4@1eE(rsS?!fr3CknP+w7O{{wL)~xZ?Yy7o zmL3HaI zPT#=_Uq7XH zoz>bm`TJaAX|$;kwz_sB(+^JpMwLQ+pCQ&7Ix^+L0w)t#fcNY*m=xcJ0I8ncWQ+n! 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