3.1.1: Resources and Key Concepts — Read

From LibreTexts, under not declared, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

Resources

Trigonometric Functions (Right Triangle Definition): For an angle \(\theta\) in a right triangle, the trigonometric functions are defined as ratios of the side opposite \(\theta\), the side adjacent to \(\theta\), and the hypotenuse. For example, \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\).
Pythagorean Triple: A set of three positive integers, \(a\), \(b\), and \(c\), such that \(a^2 + b^2 = c^2\).
Pythagorean Triangle: A right triangle whose side lengths form a Pythagorean triple.
Cofunction: Pairs of trigonometric functions consisting of sine and cosine, tangent and cotangent, and secant and cosecant. For example, the cofunction of sine is cosine.

Cofunction Identities: The value of a trigonometric function of an angle is equal to the value of its cofunction at the complement of the angle. For example, \(\sin(\theta) = \cos(90^\circ - \theta)\) and \(\tan(\theta) = \cot(90^\circ - \theta)\).

Applying Right Triangle Trigonometry to Non-Right Triangles: The right triangle definitions of trigonometric functions are only valid for angles within a right triangle. They cannot be applied to obtuse or acute triangles in general.
Confusing Exact and Approximate Values: An exact value, like \(\frac{\sqrt{3}}{2}\), is precise. A decimal approximation, like 0.8660, is a rounded value. For theoretical work, exact values are required.
Rationalizing Numerical Denominators Unnecessarily: While rationalizing is sometimes useful, expressions like \(\frac{2}{\sqrt{3}}\) are perfectly acceptable in trigonometry, and rationalizing them to \(\frac{2\sqrt{3}}{3}\) is often an unnecessary step.

This page titled 3.1.1: Resources and Key Concepts was last modified on Sun, 31 Aug 2025 22:26:56 GMT and is shared under a not declared license and was authored, remixed, and/or curated by Roy Simpson.