It's important to abide by the law. A thought-provoking lesson helps learners derive the Law of Sines. They then apply the Law of Sines to find unknown measures. 

Sal defines and explains the premise of Hubble's Law and then uses trigonometry to show the relationship between velocity and distance. He explains that as the universe expands, objects get farther away from each other; as objects move...

As a follow up to the Kahn Academy video on parallax, this video focuses on parallax as it relates to astronomical distance. Sal uses cardinal directions and the seasons to orient students in the proverbial night sky. After providing a...

Sal takes the mystery out of the trigonometric identities by showing how easily they can be derived. He continues with a problem he started in the video �Trig identities part three (part five if you watch the proofs) and proves the trig...

In this part two video, Sal finishes the trigonometric word problem of the wayward ship captain. He wisely continues the algebra work on the problem before finally turning to his calculator for the very last calculation.

In this video, Sal shows how the sine and cosine of an angle are defined on the unit circle. He inscribes a 30-60-90 triangle in the unit circle and explains how one can use SOH-CAH-TOA to find the coordinates on the circle.

Identify the variables, identify the given values and use a formula to find the missing length in this right triangle problem. What formula? The tangent ratio, which is normally used to show a ratio between two sides of a right triangle,...

A trigonometric ratio is a ratio between two sides of a right triangle. In this problem, find sin(A) in the given right triangle. Use the ratio of the opposite side over the hypotenuse.

Trigonometry? What's trigonometry. Well, something to do with triangles, right? Right! Right triangles! In this problem, find the missing length of one of the sides. So set this up as a ratio: cosine(A) = adjacent side length divided by...

Sal starts to solve a trigonometric word problem of a wayward ship captain who veers off course and once aware of his predicament, needs to know how far he is from his destination. Instead of using the Law of Cosines in his solution, Sal...

In this video, Sal derives a number of trigonometric identities. Starting with the sum of angles formula for sine and cosine, Sal proves a number of other identities including the double-angle formulas, the difference of angles formulas,...

Sal solves a challenging problem that consists of a system of three trigonometric equations and three unknowns.

In this video, Sal reviews the basic trigonometric definitions and identities including the sum of angles formulas and then derives the double angle formulas.

After defining a radian, Sal demonstrates one example of converting from degrees to radians and another example of converting radians to degrees. This video would be a good review for learners who have had prior exposure to this topic,...

Sal proves the sum of angles formula for sine, sin (a+ b) = cos (a) sin (b) + sin (a) cos (b), through a clear but rather non-intuitive proof. The proof is interesting as it not only uses the SOH-CAH-TOA model but requires one to recall...

Using a similar method that he used to prove the sum of angles formula for sine, Sal shows the proof of the cosine sum of angles formula, cos (a+ b) = cos (a) cos (b) - sin (a) sin (b). This proof also uses the SOH-CAH-TOA model and some...

If solving trigonometric equations is your idea of fun, then this video is correctly titled. Here Sal uses trigonometric identities, the quadratic formula, and inverse trigonometric functions to solve a trigonometric equation sent in by...

Sal continues with examples of finding the sine, cosine, and tangent of an angle in a right triangle using SOH-CAH-TOA. In his examples, he reviews the use of the Pythagorean Theorem and rationalizing the denominator of a fraction. He...

In an involved problem from the American Invitational Mathematics Exam from 2004, Sal logically shows the multi-step solution. He uses geometric properties of hexagons, parallelograms, and triangles, trigonometric identities, and the...

Sal solves an interesting problem from the American Invitational Mathematics Exam from 2003 that uses the Pythagorean Theorem, knowledge of geometric principles of triangles, and the use of trigonometric identities.

Sal solves a challenging trigonometric problem for finding the number of values of _ that satisfy a number of constraints over a given interval. He shows a clear step-by-step solution and uses some trigonometric identities that he derives.

Sal solves an interesting question in this video from a college entrance exam in India that requires one to use knowledge of arithmetic progressions, trigonometric identities, and algebra. He works through solving the problem in a...

In the third video on inverse trigonometric functions, Sal follows a format similar to the last two. He finds the value for the arcos (-1/2) and shows the restricted domain of the arccos function. He also finds the value for cos(arccos...

Continuing with inverse trigonometric functions, Sal finds the value for tan^-1-1. He also shows the restricted domain of the arctan function.