Trigonometry

Explore angles and the unit circle; identities and equations; triangles and oscillations. Concepts and connections are available independently of video coverage.

Prerequisites and connections

Angles
An angle measures rotation between rays sharing an endpoint.
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Angles and the unit circle

Radians
Radian measure is arc length divided by radius.
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Unit circle
The unit circle relates an angle to cosine and sine coordinates.
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Sine and cosine
Sine and cosine are the vertical and horizontal coordinates on the unit circle.
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Tangent function
Tangent is sine divided by cosine where cosine is nonzero.
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Identities and equations

Trigonometric identities
Trigonometric identities hold throughout their common domains, unlike equations requiring selected solutions.
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Angle addition formulas
Addition formulas express trigonometric functions of summed angles using individual angles.
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Inverse trigonometric functions
Restricted domains make trigonometric functions invertible with specified principal-value ranges.
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Trigonometric equations
Solutions must respect periodicity, domains and any restricted angle interval.
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Triangles and oscillations

Law of sines
In a triangle, each side divided by its opposite-angle sine has the same value.
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Law of cosines
The cosine law relates one side to the other two sides and their included angle.
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Sinusoidal models
Amplitude, frequency and phase describe a sinusoidal oscillation.
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Complex exponentials
Euler's formula links complex exponentials to cosine and sine for real angles.
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Trigonometric periodicity
Sine and cosine repeat after a full turn; tangent repeats after a half turn on its domain.
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Curriculum scope reference