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1 | 1 | { |
2 | 2 | "layout": { |
3 | 3 | "width": 620, |
4 | | - "height": 550, |
5 | | - "title": "Half-Angle Formulas" |
| 4 | + "height": 560, |
| 5 | + "title": "Half and Double Angles" |
6 | 6 | }, |
7 | 7 |
|
8 | | - "data": [{ |
| 8 | + "data": [ |
| 9 | + { |
9 | 10 |
|
10 | | - "type": "table", |
| 11 | + "type": "table", |
11 | 12 |
|
12 | | - "domain": { |
13 | | - "x": [0, 1], |
14 | | - "y": [0, 1] |
15 | | - }, |
| 13 | + "domain": { |
| 14 | + "x": [0, 1], |
| 15 | + "y": [0.5, 1] |
| 16 | + }, |
| 17 | + |
| 18 | + "columnwidth": [30, 200, 200], |
| 19 | + "columnorder": [0, 1, 2], |
16 | 20 |
|
17 | | - "columnwidth": [30, 200, 200], |
18 | | - "columnorder": [0, 1, 2], |
| 21 | + "header": { |
| 22 | + "values": [["<b>#</b>"], ["Half-angle form"], ["Equivalent"]], |
| 23 | + "align": ["right", "center", "center"], |
| 24 | + "line": {"width": 0.0}, |
| 25 | + "fill": {"color": ["dimgray", "grey"]}, |
| 26 | + "font": {"family": "Arial", "size": 14, "color": "white"} |
| 27 | + }, |
19 | 28 |
|
20 | | - "header": { |
21 | | - "values": [["<b>#</b>"], ["Form"], ["Equivalent"]], |
22 | | - "align": ["right", "center", "center"], |
23 | | - "line": {"width": 0.0}, |
24 | | - "fill": {"color": ["dimgray", "grey"]}, |
25 | | - "font": {"family": "Arial", "size": 14, "color": "white"} |
| 29 | + "cells": { |
| 30 | + "values": [ |
| 31 | + ["1.", "2."], |
| 32 | + ["$$\\cos^2\\theta=\\displaystyle\\frac{1+\\cos\\theta}{2}$$", "$$\\sin^2\\theta=\\displaystyle\\frac{1-\\cos\\theta}{2}$$"], |
| 33 | + ["$$\\cos\\theta=\\pm\\sqrt{\\displaystyle\\frac{1+\\cos\\theta}{2}}$$", "$$\\sin\\theta=\\pm\\sqrt{\\displaystyle\\frac{1-\\cos\\theta}{2}}$$"] |
| 34 | + ], |
| 35 | + "align": ["right", "center", "center"], |
| 36 | + "line": {"color": "grey", "width": 1}, |
| 37 | + "font": {"family": "Arial", "size": 12, "color": ["black"]} |
| 38 | + } |
26 | 39 | }, |
| 40 | + { |
| 41 | + |
| 42 | + "type": "table", |
| 43 | + |
| 44 | + "domain": { |
| 45 | + "x": [0.1, 0.9], |
| 46 | + "y": [0, 0.5] |
| 47 | + }, |
| 48 | + |
| 49 | + "columnwidth": [200, 300], |
| 50 | + "columnorder": [0, 1], |
| 51 | + |
| 52 | + "header": { |
| 53 | + "values": [["Trig function"], ["Double-angle form"]], |
| 54 | + "align": ["right", "left"], |
| 55 | + "line": {"width": 0.0}, |
| 56 | + "fill": {"color": ["dimgray", "grey"]}, |
| 57 | + "font": {"family": "Arial", "size": 14, "color": "white"} |
| 58 | + }, |
27 | 59 |
|
28 | | - "cells": { |
29 | | - "values": [ |
30 | | - ["1.", "2."], |
31 | | - ["$$\\cos^2\\theta=\\displaystyle\\frac{1+\\cos\\theta}{2}$$", "$$\\sin^2\\theta=\\displaystyle\\frac{1-\\cos\\theta}{2}$$"], |
32 | | - ["$$\\cos\\theta=\\pm\\sqrt{\\displaystyle\\frac{1+\\cos\\theta}{2}}$$", "$$\\sin\\theta=\\pm\\sqrt{\\displaystyle\\frac{1-\\cos\\theta}{2}}$$"] |
33 | | - ], |
34 | | - "align": ["right", "center", "center"], |
35 | | - "line": {"color": "grey", "width": 1}, |
36 | | - "font": {"family": "Arial", "size": 12, "color": ["black"]} |
| 60 | + "cells": { |
| 61 | + "values": [ |
| 62 | + ["<i>Sine</i>", "<i>Cosine</i>"], |
| 63 | + ["$$\\sin2\\theta=2\\sin\\theta\\cos\\theta$$", "$$\\begin{eqnarray*}\\cos2\\theta&=&\\cos^2\\theta-\\sin^2\\theta\\\\&=&2\\cos^2\\theta-1\\\\&=&1-2\\sin^2\\theta\\end{eqnarray*}$$"] |
| 64 | + ], |
| 65 | + "align": ["right", "left"], |
| 66 | + "line": {"color": "grey", "width": 1}, |
| 67 | + "font": {"family": "Arial", "size": [12, 10], "color": ["black"]} |
| 68 | + } |
37 | 69 | } |
38 | | - }] |
| 70 | + ] |
39 | 71 | } |
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