MATH 1316 1.4 Lecture

Reciprocal Identities00:00:39

An overview of reciprocal identities (sine/cosecant, cosine/secant, tangent/cotangent). The instructor demonstrates how to find missing values using these relationships and how to rationalize denominators.

Determining Signs of Trig Functions00:03:17

Explains how to determine the polarity of trig functions based on the quadrant of the terminal side. Emphasizes using the relationship of x, y, and r coordinates rather than memorizing tables.

Identifying Quadrants from Conditions00:10:33

Covers how to identify the correct quadrant for an angle based on given signs (positive or negative) for sine, cosine, and tangent.

Ranges of Trig Functions00:12:35

Discusses valid ranges for trig functions: sine and cosine must be between -1 and 1, while secant and cosecant must be outside the (-1, 1) interval. Tangent and cotangent have no range restrictions.

Pythagorean and Quotient Identities00:17:46

Introduces Pythagorean identities (derived from sin²θ + cos²θ = 1) and quotient identities. Demonstrates how to solve for unknown trig values using these identities when one value is provided.