Trigonometry: all 93 lessons, free

Angles and their measure

5 lessons

How an angle is named and measured once it is placed on the coordinate plane instead of inside a shape.

1.1Angles and their measure

1.2Angles in standard position and coterminal anglesPrecalculus

1.3Radian measurePrecalculus

1.4Angular and linear speedPrecalculus

1.5Arc length and sector area in radiansPrecalculus

Right triangle trigonometry

8 lessons

Ratios of sides in a right triangle, named by an angle.

2.1Opposite, adjacent and hypotenuseGeometry

2.2Right triangle trigonometry

2.3Sine, cosine and tangentGeometry

2.4Inverse trigonometric ratiosGeometry

2.5Solving right trianglesGeometry

2.6Trig values of the special right trianglesGeometry

2.7Angles of elevation and depressionGeometry

2.8Secant, cosecant and cotangent ratiosPrecalculus

Laws of sines and cosines

7 lessons

Trig for triangles that are not right.

3.1Law of sinesPrecalculus

3.2Laws of sines and cosines

3.3Area from two sides and the included anglePrecalculus

3.4Law of cosinesPrecalculus

3.5Heron's formulaPrecalculus

3.6Applications of oblique trianglesPrecalculus

3.7The ambiguous casePrecalculus

The unit circle

9 lessons

Trig for any angle, read as coordinates on a circle of radius one.

4.1The unit circle

4.2Trig functions on the unit circlePrecalculus

4.3Periodicity and the periodicity identitiesPrecalculus

4.4Reference anglesPrecalculus

4.5Secant, cosecant and cotangent on the unit circlePrecalculus

4.6Signs of the trig functions by quadrantPrecalculus

4.7Sine, cosine and tangent as functions of a real numberPrecalculus

4.8Unit circle symmetry and even-odd identitiesPrecalculus

4.9Exact values on the unit circlePrecalculus

Trigonometric functions and their graphs

16 lessons

Sine and cosine as waves, tangent as something wilder.

5.1Graphing sine and cosinePrecalculus

5.2Trigonometric functions and their graphs

5.3Amplitude and reflectionPrecalculus

5.4Amplitude, period and phase shift

5.5Finding the period from the equationPrecalculus

5.6Graphing tangent and the reciprocal functionsPrecalculus

5.7Midline and vertical shiftPrecalculus

5.8Periodic functionsPrecalculus

5.9Phase shiftPrecalculus

5.10Writing an equation from a wavePrecalculus

5.11Height on a turning wheelPrecalculus

5.12Modeling things that repeat

5.13Tides, daylight and soundPrecalculus

5.14Inverse trig functionsPrecalculus

5.15Composing trig and inverse trig functionsPrecalculus

5.16Simple harmonic motionPrecalculus

Polar coordinates and vectors

30 lessons

Direction and distance instead of x and y; quantities with a direction.

6.1Adding and subtracting vectorsPrecalculus

6.2Component form of a vectorPrecalculus

6.3Directed line segmentsPrecalculus

6.4Magnitude and direction of a vectorPrecalculus

6.5Scaling a vectorPrecalculus

6.6Unit vectors and i, j notationPrecalculus

6.7Converting between polar and rectangularPrecalculus

6.8Forces and velocities as vectorsPrecalculus

6.9Parametric equationsPrecalculus

6.10Plotting polar pointsPrecalculus

6.11Polar coordinates

6.12Polar coordinates and vectors

6.13Vector addition and scalar multiplication

6.14Vectors

6.15Vectors in spacePrecalculus

6.16Converting an equation between the two systemsPrecalculus

6.17Eliminating the parameterPrecalculus

6.18Limacons and cardioidsPrecalculus

6.19Polar circles and symmetry testsPrecalculus

6.20Polar equations and their graphs

6.21Rose curvesPrecalculus

6.22The dot product

6.23The dot product and the angle between vectorsPrecalculus

6.24Modulus, argument and polar formPrecalculus

6.25Multiplying, powers and De Moivre's theoremPrecalculus

6.26Orthogonal vectorsPrecalculus

6.27Polar form of a complex number

6.28Roots of a complex number and roots of unityPrecalculus

6.29Vector and scalar projectionPrecalculus

6.30The cross productPrecalculus

Trigonometric identities

18 lessons

Equations true for every angle, and how to use them.

7.1Cofunction identitiesPrecalculus

7.2What an identity isPrecalculus

7.3Reciprocal and quotient identitiesPrecalculus

7.4The Pythagorean identitiesPrecalculus

7.5Simplifying trig expressionsPrecalculus

7.6Solving basic trig equationsPrecalculus

7.7Verifying identitiesPrecalculus

7.8Solving trig equations by factoring, quadratics and identitiesPrecalculus

7.9Trigonometric identities

7.10Cosine of a sum or differencePrecalculus

7.11Solving trigonometric equations

7.12Trigonometric inequalitiesPrecalculus

7.13Product to sum and sum to product formulasPrecalculus

7.14Sine and tangent of a sum or differencePrecalculus

7.15Solving equations with a multiple anglePrecalculus

7.16Combining a sine and a cosine into one wavePrecalculus

7.17Double angle formulasPrecalculus

7.18Power reducing and half angle formulasPrecalculus