unit circle
Radius equals one
A unit circle is a circle with a radius of exactly one, centered at the origin of a coordinate plane.
It serves as a fundamental tool in trigonometry, where points on the circle correspond to sine and cosine values for any angle.
The unit circle shows that sine and cosine of 45 degrees are both equal to the square root of two over two.
Because the radius is one, calculations simplify elegantly, making the unit circle essential for understanding periodic functions and complex numbers.
Starting point or source
- coordinate planeTwo-axis graphing system
- quadrantFourth of a circle
- ordered pairSequence-dependent two-element set
- x-axisGraph's horizontal reference line
y-axis · point · Cartesian · polar coordinates · parametric · complex plane · intercept
Opposite over hypotenuse
- cosineRatio in triangle math
- tangentLine touching curve once
- secantTrig ratio, 1/cos
- cosecantReciprocal of sine
cotangent · radians · degrees · angle · hypotenuse · adjacent · opposite · inverse
Center-to-perimeter distance
- diameterDistance across through center
- circumferenceCircle's outer measurement
- centerMiddle of anything
- chordNotes sounded simultaneously
arc · sector · tangent line · inscribed · circumscribed · central angle · subtend · locus
Occurring at intervals
- cycleRepeating sequence of events
- revolutionViolent governmental overthrow
- oscillationRepeated back-and-forth movement
- amplitudeMaximum oscillation displacement
phase · frequency · harmonic · sinusoid · waveform · period · rotation · repetition
Circle's fundamental ratio
- radianArc-length angle unit
- tauGreek nineteenth letter
- irrationalLacking sound judgment
- transcendentalBeyond ordinary experience
origin
Starting point or source
- coordinate planeTwo-axis graphing system
- quadrantFourth of a circle
- ordered pairSequence-dependent two-element set
x-axis · y-axis · point · Cartesian · polar coordinates · parametric · complex plane · intercept
sine
Opposite over hypotenuse
cosecant · cotangent · radians · degrees · angle · hypotenuse · adjacent · opposite · inverse · arc length
radius
Center-to-perimeter distance
- diameterDistance across through center
- circumferenceCircle's outer measurement
- centerMiddle of anything
chord · arc · sector · tangent line · inscribed · circumscribed · central angle · subtend · locus
periodic
Occurring at intervals
- cycleRepeating sequence of events
- revolutionViolent governmental overthrow
- oscillationRepeated back-and-forth movement
amplitude · phase · frequency · harmonic · sinusoid · waveform · period · rotation · repetition
pi
Circle's fundamental ratio
- radianArc-length angle unit
- tauGreek nineteenth letter
- irrationalLacking sound judgment
Euler's formula
e^(ix) relates to trigonometry
- circlesradius, circumference, pie chart, ring, disk
- trigonometrysine, cosine, tangent, secant, cosecant
- topologymanifolds, compactness, neighborhoods, torus, connectedness
- precalculusfunctions, polynomials, trigonometry, logarithms, exponential functions
- complex analysiscomplex numbers, modulus, complex plane, analytic, singularity
- Mobius transformationscomplex plane, fixed points, fixed point, inversion