Intro to SOHCAHTOA

Lesson by Mike McGarry

Magoosh Expert

Summary

This content provides a comprehensive overview of the foundational principles of trigonometry, focusing on the concept of similar triangles and the introduction of SOHCAHTOA for solving problems involving right triangles.

Trigonometry is fundamentally based on the properties of similar triangles, where two triangles are considered similar if they share two equal angles, leading to proportional sides.
SOHCAHTOA is a mnemonic that helps remember the three primary trigonometric ratios: sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent), which are crucial for solving right triangle problems.
The sine, cosine, and tangent values for any given angle can be found using a calculator, enabling the calculation of unknown sides in a right triangle when one side and one acute angle are known.
The Pythagorean identity, derived from the Pythagorean theorem, states that the square of the cosine of an angle plus the square of the sine of the same angle equals one, providing a fundamental relationship in trigonometry.
Practice problems illustrate how to apply SOHCAHTOA and the Pythagorean identity to calculate unknown lengths and angles in right triangles, emphasizing the importance of recognizing patterns such as the 3-4-5 triangle.

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