Trigonometry

An introduction to trigonometric functions: sine, cosine, and tangent.

Another example of figuring out the sine, cosine, and tangent of an angle in a right triangle.

What a radian is. Converting radians to degrees and vice versa.

Using Trigonometric functions to solve the sides of a right triangle.

A couple of more examples of using Trig functions to solve the sides of a triangle.

Using the unit circle to extend the SOH CAH TOA definition of the basic trigonometric functions.

Using the unit circle to define the sine, cosine, and tangent functions.

Using the unit circle definition of the sine function to make a graph of it.

Exploring the graphs of trig functions.

Analyzing the amplitude and periods of the sine and cosine functions.

Determining the equations of trig functions by inspecting their graphs.

Determining the amplitude and period of sine and cosine functions.

Introduction to trigonometric identities.

Proof of the trig identity sin(a+b) = (cos a)(sin b) + (sin a)(cos b).

Proof of the trig identity: cos(a+b) = (cos a)(cos b)-(sin a)(sin b).

More playing around with trig identities.

Continuation of the playing around with trig identities.

The first part of a problem when the captain of a ship goes off track.

The second part of the problem of the off-track ship captain.

Introduction to the law of cosines to solve for a side of a triangle when 2 sides and an angle are known.

Trigonometry problem involving two ships colliding.

A simple proof of the Law of Sines.

Trigonometry problems dealing with the height of two people on a ferris wheel.

Part 2 of the ferris wheel problems. Graph of h(t)=9-8cos(18t).

A trig problem involving the quadratic equation.

Introduction to polar coordinates.

Conversion from Cartesian to Polar Coordinates.

Converting between Cartesian and Polar functions.

Introduction to the inverse trig function arcsin.

Understanding the arctan or inverse tangent function.

Understanding the inverse cosine or arccos function.

Revisiting the proofs of some trigonometry identities.