Pythagorean Theorem
Source of the image: https://medium.com/swlh/why-the-pythagorean-theorem-is-true-1d4c8a508510
Pythagorean theorem is one of the most remarkable discoveries in mathematics by allowing mathematicians to determine side lengths of a right triangle. This theorem is also frequently used in physics for calculating different components of a quantity.
Some useful Side Numbers
- 3, 4, 5 (9+16=25) , and any multiple of 3, 4, 5
- 6, 8,10 (36+64=100), and any multiple of 6, 8, 10
Introduction of Trigonometry
Three Sides of A Triangle
Cosine, Sine, and Tangent
By TheOtherJesse - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=2355377
Graph of cosx, sinx, and tanx
Link for cosine and sine function: https://www.desmos.com/calculator/e9nysffbhe
Link for tangent function: https://www.desmos.com/calculator/8bf7j6tfal
Trigonometry Identities Sum Up
Pythagorean Theorem and Trigonometry
Break Into Different Components
- Any quantities, such as force, velocity, etc can be break into different component by using trigonometry, and can be calculated by using the pythagorean theorem
- For the picture on the right, F can be break into a horizontal component Fx and a vertical component Fy (pythagorean theorem).
- By using trigonometry, Fx = Fcosθ, and Fy = Fsinθ. This terminology can be used physics for force component, calculating velocity, acceleration, etc
Source of the image: http://www.hk-phy.org/contextual/mechanics/for/ad_fo02_e.html