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Famous Trigonometric Values
Toolkit 57
Famous Trigonometric Values
For the following important angles:
θ
\theta
θ
sin
θ
\sin\theta
sin
θ
cos
θ
\cos\theta
cos
θ
tan
θ
\tan\theta
tan
θ
cot
θ
\cot\theta
cot
θ
0
∘
0^\circ
0
∘
0
0
0
1
1
1
0
0
0
Undefined
30
∘
30^\circ
3
0
∘
1
2
\tfrac{1}{2}
2
1
3
2
\tfrac{\sqrt3}{2}
2
3
3
3
\tfrac{\sqrt3}{3}
3
3
3
\sqrt3
3
45
∘
45^\circ
4
5
∘
2
2
\tfrac{\sqrt2}{2}
2
2
2
2
\tfrac{\sqrt2}{2}
2
2
1
1
1
1
1
1
60
∘
60^\circ
6
0
∘
3
2
\tfrac{\sqrt3}{2}
2
3
1
2
\tfrac{1}{2}
2
1
3
\sqrt3
3
3
3
\tfrac{\sqrt3}{3}
3
3
90
∘
90^\circ
9
0
∘
1
1
1
0
0
0
Undefined
0
0
0
180
∘
180^\circ
18
0
∘
0
0
0
−
1
-1
−
1
0
0
0
Undefined
270
∘
270^\circ
27
0
∘
−
1
-1
−
1
0
0
0
Undefined
0
0
0
Related Problems
Major
MathCounts 2026 Chapter Sprint Round (Problem 28)
Minor
AMC 12B 2024 (Problem 11)
AMC 12A 2024 (Problem 19)
AMC 12A 2022 (Problem 12)
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