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Precalculus — Trigonometry

Trig functions, identities, and the unit circle

T
trig_tornado 15 terms Feb 24, 2026
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Terms 15

1
sin(θ)
Opposite / Hypotenuse in a right triangle; y-coordinate on unit circle
2
cos(θ)
Adjacent / Hypotenuse; x-coordinate on unit circle
3
tan(θ)
sin(θ)/cos(θ) = Opposite / Adjacent
4
Pythagorean Identity
sin²(θ) + cos²(θ) = 1
5
sin(30°)
1/2
6
cos(60°)
1/2
7
sin(45°)
√2/2
8
cos(0°)
1
9
tan(45°)
1
10
Radian
Angle unit; 2π radians = 360°; 1 rad ≈ 57.3°
11
Unit Circle
Circle of radius 1 centered at origin; defines trig values for all angles
12
Amplitude
Half the vertical distance between max and min of trig function
13
Period
Length of one complete cycle; for sin and cos: 2π
14
Phase Shift
Horizontal shift of a trig graph; h in y = sin(x − h)
15
Law of Cosines
c² = a² + b² − 2ab·cos(C); generalization of Pythagorean theorem