Trigonometric Exact Values + Formulas
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Last updated 1:46 AM on 7/19/26
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73 Terms
1
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sin 0°
0
2
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sin 30°
1/2
3
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sin 45°
√2/2
4
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sin 60°
√3/2
5
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sin 90°
1
6
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cos 0°
1
7
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cos 30°
√3/2
8
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cos 45°
√2/2
9
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cos 60°
1/2
10
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cos 90°
0
11
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tan 0°
0
12
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tan 30°
√3/3
13
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tan 45°
1
14
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tan 60°
√3
15
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tan 90°
undefined
16
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sin θ = 0
θ = 0°
17
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sin θ = 1/2
θ = 30°
18
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sin θ = √2/2
θ = 45°
19
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sin θ = √3/2
θ = 60°
20
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sin θ = 1
θ = 90°
21
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sin θ = −1/2
θ = −30°
22
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sin θ = −√2/2
θ = −45°
23
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sin θ = −√3/2
θ = −60°
24
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sin θ = −1
θ = −90°
25
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cos θ = 1
θ = 0°
26
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cos θ = √3/2
θ = 30°
27
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cos θ = √2/2
θ = 45°
28
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cos θ = 1/2
θ = 60°
29
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cos θ = 0
θ = 90°
30
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cos θ = √3/2
θ = −30°
31
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cos θ = √2/2
θ = −45°
32
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cos θ = 1/2
θ = −60°
33
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tan θ = 0
θ = 0°
34
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tan θ = √3/3
θ = 30°
35
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tan θ = 1
θ = 45°
36
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tan θ = √3
θ = 60°
37
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tan θ = −√3/3
θ = −30°
38
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tan θ = −1
θ = −45°
39
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tan θ = −√3
θ = −60°
40
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0
0°
41
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π/6
30°
42
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π/4
45°
43
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π/3
60°
44
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π/2
90°
45
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2π/3
120°
46
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3π/4
135°
47
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5π/6
150°
48
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π
180°
49
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7π/6
210°
50
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5π/4
225°
51
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4π/3
240°
52
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3π/2
270°
53
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5π/3
300°
54
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7π/4
315°
55
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11π/6
330°
56
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2pi
360
57
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sin(360 + θ)
sinθ
58
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sin(θ-360)
sinθ
59
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sin(θ+360)
sinθ
60
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cos(90-θ)
sinθ
61
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sin(90-θ)
cosθ
62
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sin(-θ)
-sinθ
63
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cos(-θ)
cosθ
64
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tan(-θ)
-tanθ
65
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Reference Angles
90 to 180
180 - θ
66
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Reference Angles
180 to 270
θ-180
67
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Reference Angles
270-360
360-θ
68
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Finding Unknown Angle
Stand at the vertex
Find the bearings of the two sides
Subtract
Ans should be θ<180
69
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Reflection Rules
sinθ
180 - θ
70
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Reflection Rules
cosine
360-θ
71
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Reflection Rules
tangent
180 + θ
72
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sinθ is inbetween
-1 < k < 1
73
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cosθ is inbetween
-1 < k < 1