Trigonometry For Beginners!

The video introduces the fundamental concepts of right triangle trigonometry, explaining the terms opposite, adjacent, and hypotenuse relative to an angle Theta. It briefly mentions the Pythagorean theorem (a^2 + b^2 = c^2).

This section details the six trigonometric functions: sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent) as defined by the mnemonic SOH CAH TOA. It then explains their reciprocals: cosecant (1/sine), secant (1/cosine), and cotangent (1/tangent).

An example demonstrates finding a missing side of a right triangle using the Pythagorean theorem and then calculating all six trigonometric functions. The example uses a 3-4-5 right triangle, and special Pythagorean triplets are introduced (e.g., 3-4-5, 5-12-13).

Another example problem involves a right triangle with sides 8 and 17. The missing side is found, identified as an 8-15-17 special triangle, and all six trigonometric functions for the given angle are calculated.

This example presents a right triangle with a hypotenuse of 25 and another side of 15. The missing side is determined by recognizing it as a scaled version of the 3-4-5 triangle (multiplied by 5). The six trigonometric functions are then calculated, and fractions are reduced.

The video shifts to finding a missing side when an angle and one side are known. For an angle of 38 degrees, with the opposite side as 'x' and the adjacent side as 42, the tangent function is used. The calculation of 'x' requires a calculator in degree mode.

An example with an angle of 54 degrees, hypotenuse 26, and adjacent side 'x'. The cosine function is applied to find 'x', demonstrating how to use cosine when given the adjacent side and hypotenuse.

This problem involves an angle of 32 degrees, an opposite side of 12, and the hypotenuse as 'x'. The sine function is used, and the process of cross-multiplication is explained to solve for 'x'.

The video then explains how to find a missing angle when two sides are known. Using a triangle with opposite side 5 and adjacent side 4, the inverse tangent (arc tangent) function is employed to calculate the angle.

Another example of finding a missing angle, where the adjacent side is 3 and the hypotenuse is 7. The inverse cosine (arc cosine) function is used to determine the angle.

The final example for finding a missing angle involves an opposite side of 5 and a hypotenuse of 6. The inverse sine (arc sine) function is used to calculate the angle.

The presenter concludes the video by advertising his trigonometry course available on Udemy. He outlines the various topics covered in the course, including angles, radians, the unit circle, special right triangles, solving elevation/depression problems, graphing trig functions, inverse trig functions, and trig identities. He also mentions future additions to the course.