-
Notifications
You must be signed in to change notification settings - Fork 0
/
TrigonometryValues.html
181 lines (171 loc) · 7.67 KB
/
TrigonometryValues.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
<!DOCTYPE html>
<html lang="en">
<head>
<title>Trigonometry Values</title>
<link rel="icon" type="image/x-icon" href="./assets/images/favicon.ico">
<link rel="manifest" href="./manifest.json">
<script defer src="katex/katex.min.js"></script>
<script defer src="katex/contrib/auto-render.min.js" onload="renderMathInElement(document.body);"></script>
<link href="katex/katex.min.css" rel="stylesheet">
<style>
@import url(./variable.css);
* {
font-family: "Jost", sans-serif;
background-color: #d5f1f5;
text-align: center;
}
.form__field {
font-family: "Jost", sans-serif;
font-size: 1.2rem !important;
letter-spacing: 0.125rem;
width: 28%;
border: 0;
box-shadow: 0 0 10px black;
outline: 0;
margin-bottom: 1%;
color: black;
background-color: var(--appblack);
padding: 10px;
border-radius: 10px;
}
.btn {
background-color: #d5f1f5;
color: hsl(229, 84%, 12%);
border: 2px solid hsl(229, 84%, 12%);
width: 9%;
height: 46px;
border-radius: 28px;
font-size: 21px;
font-family: "Jost", sans-serif;
color: hsl(229, 84%, 12%);
}
.btn:hover {
background-color: hsl(229, 84%, 12%);
color: white;
}
form {
text-align: center;
}
h4 {
font-size: 28px;
padding: 20px;
font-weight: 800;
color: hsl(229, 84%, 12%);
text-align: center;
}
table,
th,
td {
border: 1px solid black;
margin-left: auto;
margin-right: auto;
}
li {
font-size: 21px;
font-weight: var(--fw-8);
color: var(--oxford-blue);
line-height: 1.3;
}
</style>
</head>
<body>
<div class="stopwrap">
<table class="table table-bordered table-dark">
<thead>
<tr>
<th scope="col">\[Angles→\]<br>\[Ratios↓\]</th>
<th scope="col">\[0^{\circ}\]</th>
<th scope="col">\[30^{\circ}\]</th>
<th scope="col">\[45^{\circ}\]</th>
<th scope="col">\[60^{\circ}\]</th>
<th scope="col">\[90^{\circ}\]</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">\[\sin\theta\]</th>
<td>\[0\]</td>
<td>\[\frac{1}{2}\]</td>
<td>\[\frac{1}{\sqrt{2}}\]</td>
<td>\[\frac{\sqrt{3}}{2}\]</td>
<td>\[1\]</td>
</tr>
<tr>
<th scope="row">\[\cos\theta\]</th>
<td>\[1\]</td>
<td>\[\frac{\sqrt{3}}{2}\]</td>
<td>\[\frac{1}{\sqrt{2}}\]</td>
<td>\[\frac{1}{2}\]</td>
<td>\[0\]</td>
</tr>
<tr>
<th scope="row">\[\tan\theta\]</th>
<td>\[0\]</td>
<td>\[\frac{1}{\sqrt{3}}\]</td>
<td>\[1\]</td>
<td>\[\sqrt{3}\]</td>
<td>\[Not \space Defined\]</td>
</tr>
<tr>
<th scope="row">\[\cosec\theta\]</th>
<td>\[Not \space Defined\]</td>
<td>\[2\]</td>
<td>\[\sqrt{2}\]</td>
<td>\[\frac{2}{\sqrt{3}}\]</td>
<td>\[1\]</td>
</tr>
<tr>
<th scope="row">\[\sec\theta\]</th>
<td>\[1\]</td>
<td>\[\frac{2}{\sqrt{3}}\]</td>
<td>\[\sqrt{2}\]</td>
<td>\[2\]</td>
<td>\[Not \space Defined\]</td>
</tr>
<tr>
<th scope="row">\[\cot\theta\]</th>
<td>\[Not \space Defined\]</td>
<td>\[\sqrt{3}\]</td>
<td>\[1\]</td>
<td>\[\frac{1}{\sqrt{3}}\]</td>
<td>\[0\]</td>
</tr>
</tbody>
</table>
<h2>\[Values \space of \space some \space T-Ratios \space for \space many \space angles \]</h2>
<p>\[1) \space sin(7.5^{\circ})= \frac{\sqrt{2-\sqrt{2+\sqrt{3}}}}{2}= cos(82.5^{\circ})= sin \frac{\pi}{24}\]
</p>
<p>\[2) \space cos(7.5^{\circ})= \frac{\sqrt{2+\sqrt{2+\sqrt{3}}}}{2}= sin(82.5^{\circ})= cos \frac{\pi}{24}\]
</p>
<p>\[3) \space tan(7.5^{\circ})= \sqrt{6}-\sqrt{3}+\sqrt{2}-2=(\sqrt{2}-1)(\sqrt{3}-\sqrt{2})= cot(82.5^{\circ})= tan\frac{\pi}{24}\]</p>
<p>\[4) \space cot(7.5^{\circ})= \sqrt{6}+\sqrt{3}+\sqrt{2}+2=(\sqrt{2}+1)(\sqrt{3}+\sqrt{2})= tan(82.5^{\circ})= cot\frac{\pi}{24}\]</p>
<p>\[5) \space sin15^{\circ}= \frac{\sqrt{3}-1}{2\sqrt{2}}= cos75^{\circ}= sin \frac{\pi}{12}\]
</p>
<p>\[6) \space cos15^{\circ}= \frac{\sqrt{3}+1}{2\sqrt{2}}= sin75^{\circ}= cos \frac{\pi}{12}\]
</p>
<p>\[7) \space tan15^{\circ}= 2-\sqrt{3}= cot75^{\circ}= tan\frac{\pi}{12}\]</p>
<p>\[8) \space cot15^{\circ}= 2+\sqrt{3}= tan75^{\circ}= cot\frac{\pi}{12}\]</p>
<p>\[9) \space sin18^{\circ}= \frac{\sqrt{5}-1}{4}= \sqrt{\frac{3-\sqrt{5}}{8}} = cos72^{\circ}= sin\frac{\pi}{10} \]</p>
<p>\[10) \space cos18^{\circ}= \frac{\sqrt{10+2\sqrt{5}}}{4}= \sqrt{\frac{5+\sqrt{5}}{8}} = sin72^{\circ}= cos\frac{\pi}{10} \]</p>
<p>\[11) \space tan18^{\circ}= \sqrt{1-\frac{2\sqrt{5}}{5}}= cot72^{\circ}= tan\frac{\pi}{10}\]</p>
<p>\[12) \space cot18^{\circ}= \sqrt{5+2\sqrt{5}}= tan72^{\circ}= cot\frac{\pi}{10}\]</p>
<p>\[13) \space sin(22.5^{\circ})= \frac{\sqrt{2-\sqrt{2}}}{2}= \sqrt{\frac{4-\sqrt{8}}{8}} = cos(67.5^{\circ})= sin\frac{\pi}{8}\]</p>
<p>\[14) \space cos(22.5^{\circ})= \frac{\sqrt{2+\sqrt{2}}}{2}= \sqrt{\frac{4+\sqrt{8}}{8}} = sin(67.5^{\circ})= cos\frac{\pi}{8}\]</p>
<p>\[15) \space tan(22.5^{\circ})=\sqrt{2}-1=cot(67.5^{\circ})= tan\frac{\pi}{8}\]</p>
<p>\[16) \space cot(22.5^{\circ})=1+\sqrt{2}=tan(67.5^{\circ})= cot\frac{\pi}{8}\]</p>
<p>\[17) \space sin36^{\circ}= \frac{\sqrt{10-2\sqrt{5}}}{4}= \sqrt{\frac{5-\sqrt{5}}{8}}= cos54^{\circ}= sin\frac{\pi}{5}\]</p>
<p>\[18) \space cos36^{\circ}= \frac{\sqrt{5}+1}{4}= \sqrt{\frac{3+\sqrt{5}}{8}}= sin54^{\circ}=cos \frac{\pi}{5}\]
</p>
<p>\[19) \space tan36^{\circ}= \sqrt{5-2\sqrt{5}}= cot54^{\circ}= tan \frac{\pi}{5}\]
</p>
<p>\[20) \space cot36^{\circ}= \sqrt{\frac{5+2\sqrt{5}}{5}}= tan54^{\circ}= cot \frac{\pi}{5}\]
</p>
<p>\[21) \space sin(37.5^{\circ})= \frac{\sqrt{2-\sqrt{2-\sqrt{3}}}}{2}= cos(52.5^{\circ})= sin \frac{5\pi}{24}\]
</p>
<p>\[22) \space cos(37.5^{\circ})= \frac{\sqrt{2+\sqrt{2-\sqrt{3}}}}{2}= sin(52.5^{\circ})= cos \frac{5\pi}{24}\]
</p>
<p>\[23) \space tan(37.5^{\circ})= \sqrt{6}+\sqrt{3}-\sqrt{2}-2=(\sqrt{2}+1)(\sqrt{3}-\sqrt{2})= cot(52.5^{\circ})= tan\frac{5\pi}{24}\]</p>
<p>\[24) \space cot(37.5^{\circ})= \sqrt{6}-\sqrt{3}-\sqrt{2}+2=(\sqrt{2}-1)(\sqrt{3}+\sqrt{2})= tan(52.5^{\circ})= cot\frac{5\pi}{24} \]</p>
</div>
</body>
</html>