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Trig Identities Part 3 (Part 5 If You Watch the Proofs), Trigonometry
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...
Curated OER
Trigonometry Work Problems (Part 2)
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.
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Introduction to the Unit Circle, Trigonometry
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 to use SOH-CAH-TOA to find the circle's coordinates.
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Trigonometry Word Problems (Part 1)
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...
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Trigonometric System Example, Trig Identities and Examples, Trigonometry
Sal solves a challenging problem that consists of a system of three trigonometric equations and three unknowns.
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Trig Identities Part 2 (Part 4 If You Watch the Proofs)
In this video, Sal reviews the basic trigonometric definitions and identities, including the sum of angle formulas, and then derives the double angle formulas.
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Proof: sin(a+b)=(cos a)(sin b)+(sin a)(cos b)
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 uses the SOH-CAH-TOA model and requires one to recall some...
Khan Academy
Proof: cos(a+b)=(cos a)(cos b)-(sin a)(sin b)
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...
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Polar Coordinates 1, Parametric Equations and Polar Coordinates, Precalculus
Sal defines polar coordinates and the relationships between Cartesian coordinates and polar coordinates using basic trigonometric identities and the Pythagorean Theorem in this introductory video.
Khan Academy
Fun Trig Problem
If solving trigonometric equations is your idea of fun, then this video is correctly titled. Sal uses trigonometric identities, the quadratic formula, and inverse trigonometric functions to solve a trigonometric equation sent in by a...
Khan Academy
IIT JEE Trigonometric Constraints, Trig Identities and Examples, Trigonometry
Sal solves a challenging trigonometric problem for finding the number of values of _ that satisfy several constraints over a given interval. He shows a clear step-by-step solution and uses some trigonometric identities that he derives.
Khan Academy
IIT JEE Trigonometry Problem 1, Trig identities and Examples, Trigonometry
In this video, Sal solves an interesting question from a college entrance exam in India that requires knowledge of arithmetic progressions, trigonometric identities, and algebra. He works through solving the problem step-by-step by...
Khan Academy
Inverse Trig Functions: Arccos, Trigonometry
Sal follows a format similar to the last two in the third video on inverse trigonometric functions. He finds the value for the arccos (-1/2) and shows the restricted domain of the arccos function. He also finds the value for cos(arccos...
Khan Academy
Inverse Trig Functions: Arctan, Trigonometry
Continuing with inverse trigonometric functions, Sal finds the value for tan^-1-1. He also shows the restricted domain of the arctan function.
Khan Academy
Inverse Trig Functions: Arcsin, Trigonometry
Sal defines the concept of inverse trigonometric functions and completes two examples of arcsin. Specifically, he finds the values of the arcsin (sqrt 2/2) and arcsin (sqrt 3/2). He also discusses the restricted domain of the arcsin...
Curated OER
Fun Trig Problem
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...
Khan Academy
Ferris Wheel Trig Problem (Part 2)
Sal continues the Ferris wheel problem in a previous video by graphing the function between zero and 30 seconds.
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Ferris Wheel Trig Problem
The next time you are at an amusement park you may want to consider all the interesting math problems you could do! Using trigonometric ratios, some logic and algebra, Sal solves a problem in this video of finding a person's height off...
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Proof: Law of Sines, Trig Identities and Examples, Trigonometry
Sal proves the Law of Sines in this video by using the SOH-CAH-TOA model and setting up equivalent ratios.
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Proof of the Law of Cosines, Trig Identities and Examples, Trigonometry
Sal derives the Law of Cosines using a method similar to the wayward ship captain word problem he solves in another video. This video provides a good review of using the SOH-CAH-TOA model, the Pythagorean Theorem, some basic trig...
Curated OER
Trigonometry work problems (part 2)
In this part 2 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.
Curated OER
Proof: cos(a+b)=(cos a)(cos b)-(sin a)(sin b)
Using a similar method that he used to prove the sum of angles formula for sine, Sal shows the proof 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...
Curated OER
Intro to the Trigonometric Ratios
This video introduces the basics of trigonometry. It starts by defining a right triangle and showing two different examples of finding the ratios of sine, cosine, and tangent using the SOH-CAH-TOA mnemonic. This resource could be used as...
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Hubble's Law, Scale of the Universe, Cosmology and Astronomy
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...