From 3b4787f4c48b5720d340ffdba390f5be2c6ae798 Mon Sep 17 00:00:00 2001 From: zleyyij <75810274+zleyyij@users.noreply.github.com> Date: Fri, 13 Sep 2024 16:18:00 -0600 Subject: [PATCH] vault backup: 2024-09-13 16:18:00 --- Pasted image 20240911131855.png | 0 .../math/MATH1060 (trig)/The Unit Circle.md | 9 +++++---- .../math/MATH1060 (trig)/assets/unitcirc.png | Bin 0 -> 157192 bytes 3 files changed, 5 insertions(+), 4 deletions(-) delete mode 100644 Pasted image 20240911131855.png create mode 100644 education/math/MATH1060 (trig)/assets/unitcirc.png diff --git a/Pasted image 20240911131855.png b/Pasted image 20240911131855.png deleted file mode 100644 index e69de29..0000000 diff --git a/education/math/MATH1060 (trig)/The Unit Circle.md b/education/math/MATH1060 (trig)/The Unit Circle.md index ab81a81..fe7e171 100644 --- a/education/math/MATH1060 (trig)/The Unit Circle.md +++ b/education/math/MATH1060 (trig)/The Unit Circle.md @@ -11,10 +11,11 @@ $$ cos(\theta) = x $$ $$ sin(\theta) = y $$ ## Sine and Cosine -| Angle | $0$ | $\frac{\pi}{6}$ or $30 \degree$ | $\frac{\pi}{4}$ or $45\degree$ | $\frac{\pi}{2}$ or $90\degree$ | -| ----- | --- | ------------------------------- | ------------------------------ | ------------------------------ | -| | | | | | -| | | | | | +| Angle | $0$ | $\frac{\pi}{6}$ or $30 \degree$ | $\frac{\pi}{4}$ or $45\degree$ | $\frac{\pi}{2}$ or $90\degree$ | +| ------ | --- | ------------------------------- | ------------------------------ | ------------------------------ | +| Cosine | 1 | $\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | +| Sine | 0 | $\frac{1}{2}$ | $\frac{\sqrt{2}}{2}$ |
$1$ | +![image]() ## The Pythagorean Identity The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions. diff --git a/education/math/MATH1060 (trig)/assets/unitcirc.png b/education/math/MATH1060 (trig)/assets/unitcirc.png new file mode 100644 index 0000000000000000000000000000000000000000..df661c5b91d04299b541f3c88c2247d4c0b69925 GIT binary patch literal 157192 zcmeFYWmp_r(=Ln!2>}KV?hqis-CcsaySrO(cL{{x!Gc@x;I6^loq^!)@-=%u@7{UN zcmAG#?_Af=J>5&XYt^c%`>rBfURE6GHSTK&2nZxe2@ypI2xw#o2&g!CSl|kq#)m-& zh&Qqp!ou>B!otMzj&`ON)+P`T65)wzaOz3}Sl_f1Nnqeb1U~M{fIg!Me1!jS5kpKv zf&ls$g&^1yLs!10iHiE3w()h&93(2Z>OEM z=k(j1bf=w_255+u1o}j9PAbHfi z*JpQ>0$&bU;qqqq@1L#4(IU2>AmYr!CW9RX3A;lf+qGa6HTWPzsJDjAwxtq(zA+@g zaRzPRQj93CV^PSetJ8C!E80?6o+Ftc!+r+>_n(18_Wo9O4fJ)^XEJr_ey5a57TmH$@HYwe5Lw95= z_33J3lFGqkgOzVvL-0z5E@7)5C&+S%XJ8?EdO8I?DNIeNh0v6*3Zn%^f;pk3!>9(F zHr<82O5=z?u$3g;IPpvUCnRY(Zye$#V8JM5pq=v#l9|AtV&o`McvYMfX{g*h$HQ-M zl9;>Q&P@XO-d*z3I-+sVcuR9jb>mI+;UiXWBoOBd;mZ@tMg^%uZ%BB^YR|>VSQ=ol zJI;yahpF@$LRLzXBV4KdHrmFi%9Acw9l zh@Gd7n21g`kx%#iaBPg)ZMd50xp1z^)7rft$65eHJJf6S$&NR1NZp4m(Jd#k)95fa z0E8sB%o+jU^4up$yOix1^zqzDVacox# zI~RD{AAB7lNHGuw7rusI-2HqKhEf928;4j@^}KrCb$}fLopM4V#>hh!$!9J3h8z|o z9408DwFGh9(Q;z%ei=B8W41}y<=|CG#Y5o?B1E+XaUrDomf`}K5YqPj9YBz~47!(xn4ulfl!LsX( zrM<(%fH(vlDaiQlRY}Jud4#%v!z|c?S8#%4=8y#)v1@2Qp=|w{>@S`Dcd}5LVTnL6 zBqS_B{<~z9VHAe39Awtra0nuupVi56B!!t!5po2;BvNsT#vc^Jt%WT=L-#9eu{fgs z7C0hC`AoPax5XQgy;q2A8KjxLslYZU*fr+vOp_WuB7!)cxBIaMs!Z%U3u)Kl0__v@ zp-5)#-pe5m*99I=-z*uAx$*Ga*#N_XIh1%66i5a^BFn zpz5NBi%^cI?jo=D7#p%V&^f$vV0Iun#i$ItNuHA<{d^&LMQ*2v5iU1Kg_*z>e-$Si zUmo8mVK-oDj9$ge8I~^eH7>G$duw?MeXC^4YzqZLCW4|T0ZkND5iGB&;3}U=okXqk z1x5KoG3#_1uH0}wUB0UPe$h_hbz#NS)YQ-v&y?X*w`JrM&D2$ij=X2#m8_1|vTR1l zx8ibny`omB$1isTmuf7y!x3O{sqF1Z)d@=rGjkMkJJz?jF}OTP*}X#1G|{lpCAjpv z7>yJe!kJ?9-;*X$#_1U9s3f)MP(PKy(Oam4K%Yg40#f&(NM2x=177;nQ4B@p@e)9Q5+Je^N{fYfz zWxx6Y`qJrQc9(r`mAxJ5;EmxMQygnX4zn?CRkPAr^^UptO1Qo!!!XXh1YYc00)&+Ct-on{rivzQC8*Njs&Yyij1{+4CY}Cx07H4=;Nj(PJRW#~m8s7OK z`6T(TCvEZ%^NEH^htY;2hOSbU*$Yyuhna_d4QUPEzn6Yb`W~z?rSV`WS!t|gs$u(s z$L_XwaDisPGDRguBRx)Tag>r?4#z^)UZIIp|3rV3fS~}Uz`cOG0G+@c*v!`?K|#T# z2n{{V8wl>T&8_m+W4GC6T~l2foits9!HdDaI@8F;!p6c}P_IcpkWqY&Rv?bRuBF@a zsd2d&+BIVAPTox}PA;fKH{9v@7HiZk6T3)o&9%bsqw=r}lLjLyWJSu$$XdyEDx)Yc zvG9FlV3TSz(~EkZSR;Mui_k|&>G_liehT}+J8GSx@}iz1_5w}04BpEPmOzV!$r!l; zxg9zFFJcl>9~U#OJ`?p+fUgVAC)o3@5q<_B1?&j%8>IXY-}<0Q`|0a?MkQM=_awKI zj;Y*NJ5>+Wie%byjJ6@0qbd7lR|B2K+}mMZ#m&@ua8JAS)YcfQ?+CGOFqAQyGZH!W$E?fdkfG z?~z-Txhdah@=wH}T~uo*Tc}F?sabUg#$9D)wW^)LD)(-tGt?2rDJlJaP;ogqtM}fG zdbQENQLr+*nzT8`BDbe^8joMqRAr^`tYV>lz<%;f#*PhOjl+SyF%= z-;$1VtbN5+EBNsYE(E36xAxIRuRv?(G!znLk+6ri@m~Gp<`(@nAy!8!bK=`qer6BV z#lxlL3G^wa?Rx4q7v3bk=P|8^rkUe3-MMCthtO3b8}EesM%_VOE%dQ#%QnmAkWlB&zd6ARlpnh>+mG0-uP^1UV| zCgyQ8Hsw+j5&KVf;1@5cxwEr97d^e3n;V@QGo78I89gH>Cnr4v6Fn2t2cX3VCl6a^ z1NRTMPGo-%@;~ECc{j-1$FysyLZA3ftKLQ#$kgyIlY2{O8U8bmXCbdGkLc@wb@&x(djd?==toKWoPK z+Hm`w0I-bs79w)Wz!6Zgmk*=_@aNs%N8lV1dIV&1Jq`gO03j(NsO%1TkOAjMU~+jS zcb9MdsiG+^Xw37t#f=X`UhoU0D@gQJM;lTPEStzHLDcWX&LC=1neW1dk`l))^~Vn@ z4Q46YuGdGDO#`-9DO*QF&F6I<;E{~;A&WBAdqd42KM)8?NB|xll7txMuOGF+zZwHSzK95PXOoK*|EK%Ew}Hmc|Ni=Wn*VM5kDUKkbbo5y z|4QS3rSTsd^uKoFPmBEjRvLJ(pi0y#WOv4kRZ411`3K+WbI0VpelnY{GGR07eM3u6 zUtg}%l)tgTrJ!c@KOO?ut2NFrBKVqj?D}LJ&pd(xC!wGy9OhnK_w`qJ?6&D;+6@y6 zbv9`uEPGYDRmS0Enze&5{7>$Su8TI44hxYy)-ZanGXnncJY#F{VH_+R-}mgj$w0<_ z4kXZ{Jm*o%zR!W~Sz)HC_Kt!H)IYMDoQ zCfQcK&RGr(C*+&kT1RCz5&pHaSw+Oe8)M4lLEuVN_$|q<2uxb*jqY&QQQqsh&S1nc znKU-nRqtyJ6O%jwpPTjY_dI9)WLIOtDD$%1hsL4!j$t;{!)&Sw3I+t+uBEs{RiMWR z4&{yCebbDbB4~n<_CT7MM+kY zQo8MS*zRD(^SIV>JeU>-Tp{1mU>gUGA$iZq?Mbf22YTGxG`(HPl5=&L#~83jW4R zsNF2O7c#*9df9EUsNkC=9HF~DDaP})@3Wa*+hd*gCf=$

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